Lord Jagannath is worshiped along with Balbhadra and Subhadra in the famous temple at Puri. I want to know is Lord Jagannath an incarnation of Vishnu?
Yes he is. Section 1.2.11 of the Skanda Purana mentions the same:
While describing the majesty of Purushottam kshetra, goddess Laxmi revealed to lord Brahma--' In the coming satya yuga there would be a king named Indradyumna and would be famous for his unflinching devotion in lord Vishnu. Being pleased by the king's devotion, lord Vishnu would ultimately manifest himself from a wooden structure to bless him. Vishwakarma would then carve out four idols (Jagannath, Balbhadra, Subhadra and Sudarshan chakra) from the wooden block all of which would be installed by none other than you (Brahma).'
The rest of the story is detailed in Skanda Purana Vaishnava Khanda - Purushottama Kshetra Mahatmya
Introduction: In Kritayuga, there was a great king named Indradyumna. He was righteous and belonged to the Solar dynasty, and was the fifth descendant from Lord Brahma. He was a devotee of Lord Vishnu and very truthful. His capital was Avanti in the Malava country.
Enquiry about visible manifestation of Lord Jagannatha: Once in an assembly of learned brahmanas and pilgrims he asked his priest whether Lord Jagannath exists visibly in any place. The priest asked the assembly of pilgrims. A certain widely travelled pilgrim told about Sri Purushottama in Odhra desa on the southern shore sea of Bharata. There is a mountain names Nilagiri surrounded by forests. In the middle of the forest there is a kalpa tree extending a krosha whose shade dispels sins. To the west is a holy pool named Rauhina filled with primordial waters which bestows salvation. On the eastern bank Lord Jagannatha visibly exists holding conch, discus and club. On the western side the sabaras (hunter community) live in hermitage known as sabara dipika. The place is so holy that heaven dwellers come there every night to worship the Lord. There is also a legend about a crow getting liberated there. Saying this the pilgrim vanished.
Vidyapati travelling to Sri Purushottama: Hearing this the king intended to settle there with his entire kingdom and worship Lord Jagannatha. In consultation with the priest he sent the younger brother of the priest named Vidyapati to locate the place and also find a suitable place of residence. On an auspicious day Vidyapati left in a chariot with emissaries.
Vidyapati reaching Mahanadi: Vidyapati considered himself highly fortunate to be able to see the Lord with his own eyes. Towards the end of the day he reached the bank of river Mahanadi at Odhra. He performed his evening rites meditating on the Lord and spent the night in the chariot.
Vidyapati crossing Mahanadi and reaching Ekamraka vana and Nila mountain: Early in the morning Vidyapati crossed the river Mahanadi and saw the villages of Vedic brahmanas. He then crossed the Ekamraka forest and came to the Nila mountain. He climbed the top of the forested mountain but could not locate the path further. He spread darbha grass on the ground and meditated on the Lord. Then Vidyapati heard some voices discussing about the Lord. He saw Sabaradipika surrounded by the house of Sabaras.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 7 - 8): Vidyapati meeting sabara Vishwavasu and seeing the Lord: Then Vidyapati approached a sabara named Vishwavasu who welcomed him and asked about his purpose. Vidyapati told him about the mission of king Indradyumna and his own eagerness to see the Lord. Vishwavasu was initially worried because the sabaras were secretly worshipping the Lord. But he remembered a traditional legend that in future the Lord will vanish and a king named Indradyumna will perform hundred horse sacrifices and install the wooden form of the Lord. Thinking that the time has come for this legend to come true, he took Vidyapati through rugged mountain forest to the holy pool Rauhina. To the east was the great Kalpa banyan tree and between these two was the presence of the Lord. Vidyapati took his bath in the holy pool and eulogized the Lord with ecstasy. Towards the evening they returned to the hermitage of Vishwavasu. Vishwavasu offered a warm hospitality to Vidyapati with the Nirmalya (remnants of the worship of the devas) of the Lord. Vidyapati was surprised. Next day in the early morning, they took bath in the ocean and Vishwavasu showed the idol of Nilamadhava to Vidyapati.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 9 - 10): Vidyapati returning and the Lord vanishing: After deciding about a place of residence for the king, Vidyapati left for Avanti. In the meantime a violent gust of wind raised the sands of the sea shore and submerged the Lord along with the Rauhina kunda. The devas became highly sorrowful and lamented. Vidyapati returned to Avanti and reported everything to the king. The king was overjoyed. At the sametime sage Narada visited the king and stayed with him to guide the king in the great journey.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 11): Indradyumna starting for Purushottama Kshetra: Indradyumna proclaimed to his entire kingdom to get ready to go to Purushottama Kshetra. The king departed on the auspicious day of Jyestha Shukla Paksha Panchami (a Wednesday). The entire kingdom accompanied him.
Indradyumna reaching the shrine of Carcika on the boundary of Utkaladesa: The king passed through various lands and forests and reached the shrine of Carcika (Goddess Durga) at the boundary of Utkaladesa. At the behest of sage Narada, the king got down the chariot and eulogized the Devi.
Indradyumna camping at the bank of river Chitrotpala and meeting the king of Utkala: Later on, the king camped at the bank of river Chitrotpala (Mahanadi) and performed his evening rites. During this stay the king of Utkala came to meet him with various gifts. King Indradyumna welcomed him and in the course of the conversation came to know that the idol of Madhava has been covered by a sandstorm. When the king left, Indradyumna was highly dejected but sage Narada consoled him saying that he will certainly see the Lord.
Indradyumna crossing river Mahanadi and going towards Ekamravana: Next morning after performing the religious rites the king started the journey. He crossed the river Mahanadi and proceeded towards Ekamravanaka (modern Bhuvaneshwar). The king of Odhra showed the way.
Indradyumna reaching the river Gandhavaha and the shrine of Kotilingeshwara: After travelling some distance the king reached the river Gandhavaha and heard the sound of the forenoon worship of the Kotilingeshwara shrine. The Nila mountain was three yojanas from there. The king took bath in the Bindu Tirtha and worshipped the idol of Purushottama installed on the bank. Then he visited the temple of Koteshwara and sang devotional songs accompanied by Veena. Lord Koteshwara through a voice told the king that his desire will be fulfilled. Through another voice the Lord Koteshwara told sage Narada to guide the king to perform the horse sacrifices as per the command of the Lord.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 12 - 14): Indradyumna reaching Kapotesha and Bilvesha: The next day the king reached the shrines of Sri Kapotesha and Bilvesha and worshipped them. Proceeding further the king reached the boundary of the holy place of Nilakantha. Then bad omens began to appear before him. Sage Narada told the king that the deity had vanished below the sand and he will not be able to see Nilmadhava. The king fell on the ground unconscious. Bringing back his consciousness, sage Narada told the king about the prediction of Lord Brahma and urged the king to perform the horse sacrifices at Purushottama Kshetra. Indradyumna's grief was dispelled.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 15): Indradyumna climbing the Nila mountain; seeing the idol of Nrisimha and the former place of Nilamadhava: The king left the chariot behind and worshipping Mahadeva and Devi Durga climbed the difficult terrain of the Nila mountain. Sage Narada guided the king to the place where the Lord was residing as Nrisimha. The idol was of extremely terrible form and the king bowed to the Lord from a distance. Then he enquired the sage about the former place of Nilamadhava. When sage Narada showed him the spot, the king prostrated on the ground and eulogized the Lord with deep devotion. An ethereal voice assured the king that the Lord will be visible to him later and urged him to carry out the direction of Brahma as mentioned by Narada. King Indradyumna was assured and decided to perform the horse sacrifies.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 16): King Indradyumna building a shrine and sage Narada installing Nrisimha at the place of the horse sacrifice: Then sage Narada invoked the celestial architect Vishwakarma, and instructed the king to build a shrine for Nrisimha at the place of horse sacrifice with the help of Vishwakarma (this was completed in four days). Narada himself got a second idol of Nrisimha built by Vishwakarma and meditating for five days infused this idol with the prana of the original Nrisimha idol. Then he installed this idol of Nrisimha on Jyestha Shukla Paksha Dwadashi in conjunction with the Swati Nakshatra. King Indradyumna eulogized Nrisimha with various hymns.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 17): King Indradyumna performing thousand horse sacrifices: Then the king constructed sacrificial halls and the houses for the guests and invited all the devas and thousand of sages and brahmanas. He made elaborate arrangements for them and extended a grand hospitality. He beseeched the favour of Indra deva to ensure that the sacrifice is completed without obstacles. The devas assured their full support for this work of Madhava. The king started performing the horse sacrifices as per the prescribed rules of the scriptures. Gradually all but the last sacrifice remained to be performed. The king had a vision of Lord Vishnu in the milky ocean. He eulogized the Lord with tears of joy.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 18): Emerging of a celestial tree: On the last day of the last sacrifice when the Sutya rite (extraction of Soma) was being performed, the servants reported to the king that a celestial tree was seen at the sea shore whose fragrance spreads across the whole surroundings. Sage Narada told the king that the hair of Sri Vishnu had incarnated as the tree. He instructed the king to complete the horse sacrifice and install the tree in the sacrificial altar. When the tree was installed, an ethereal voice told the king to conceal the sacrificial altar for fifteen days during which time a carpenter will build the divine idols of the Lord. Music should be played during this time to hide the sound of carving.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 19): Carving of the idol of Purushottama: Sri Vishnu assumed the form of an old carpenter and started carving the idol of the Lord. During this work divine fragrance, divine music and shower of parijata flowers took place. After the work was over, an ethereal voice gave instructions about how the idols should be painted and decorated. When the king unveiled the altar he saw the divine idols of Krishna (Jagannatha), Balarama and Subhadra. The king was immersed in a joy of bliss and stood there motionless. All his exertions had finally became fruitful. The king eulogized the Lord and prostrated before Him. Sage Narada and other sages also eulogized the Lord.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 27): Lord Brahma installing the deities: When all the arrangements for installation of the deities were completed, Lord Brahma Himself came down from Satyaloka. He eulogized Narayana, Balarama, Subhadra and Sudarshana and ceremoniously installed the deities from the chariots inside the shrine. The installation was performed on Vaisakha Shukla Paksha Ashtami on a Thursday in conjunction with the Pushya nakshatra.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 27 - 28): Lord assuming the form of Narasimha: After installing Madhava, Lord Brahma repeated the Mantraraja a thousand times. By the power of that Mantra, the Lord assumed the terrible form of Narasimha with a blazing tongue as if licking the entire universe. Upon enquiry by sage Narada, Lord Brahma said that this mantra was used previously by Brahma when the Lord killed the demon Hiranyakasapu. Then Lord Brahma eulogized Narasimha and initiated king Indradyumna in that mantra.
Skanda Purana (Vaishnava Khanda - Purushottama Kshetra Mahatmya 29): Granting of boon to Indradyumna: Thereafter Lord Brahma took away the Narasimha form and idols were seen as before. Lord Brahma requested Madhava to bless the king to be able to continue His worship with devotion. The wooden body of Lord Madhava then directly blessed king Indradyumna with boons. Madhava blessed that his devotion will be steady and He (i.e. Madhava) will never abandon that place even if the shrine crumbles.
Lakshmi's mention of Lord Vishnu appearing as Jagannatha and the repeated association of Narsimha to the idols testifies that it was Lord Vishnu Himself who appeared as Lord Jagannath.
Yes, Lord Jagannath is Krishna, and thus an avatara of Vishnu!
This is the legend of Puri Jagannatha temple -
After the demise of Lord Krishna at the tail end of Dwapara yuga, and towards the commencement of kaliyuga, his heart alone kept throbbing and panchapandavas threw this heart in the ocean. One tribal king called Vishwavasu Sabara found this heart when he was fishing deep in the ocean, and amazingly, as soon as he found it, it turned it into an idol worthy of worship and he kept in a sacred spot calling it 'Neela Madhava' and worshiped it!
In the meantime, there was an eminent king of the North, Orissa area who was on the lookout for a suitable idol for his newly constructed temple and sent his knights in all four directions looking for the same! One minister of his, called Vidyapathi, reached the place of Vishwavasu Sabara, stayed with Sabara, fell in love with his daughter and married her. After that, he noticed his father-in-law, Sabara, was mysteriously going and returning from some place each morning and on pestering, learnt from Sabara, about the neelamadhava idol. Deciding that this idol is the one that would most certainly please his king, after visiting this idol and making sure of its eminence, he went to his king and informed him about the idol!
The king immediately set out to the place of Sabara. He tried to go see the statue of Neelamadhava, but the statue, upon him reaching the sacred spot, had disappeared. He felt very sad. But an echo from the sky reassured that he will get a different form of a statue for a compensation.
Soon, on the shores, a large sandalwood block washed ashore. Nobody could sculpt it, it just could not be pierced. But, divine sculptor Viswakarma visited the king in the demise of an old sculptor and promised to sculpt elegant statues of the Lord, if promised nobody would peek into what he was doing. The king agreed.
After sometime, the queen became impatient, and took a peek through the doors to see what the old sculptor was doing. Immediately, the sculptor vanished. When everyone came in to see what happened, they found the statues of Balabadra, Subadra and Jagannatha!
This is the story of Lord Jagannath. As you can see, from the facts that Neelamadhava was Lord Krishna's heart and the divine voice assured to give the new statues in replacement for the lost Neelamadhava statue, it can be assured that Lord Jagannatha is none other than Krishna!
This is the legend, as I read it in the internet. One such site, which explains about Lord Krishna's heart is :