I never heard this story before, but I'm curious to know about this.
Why Shiva burnt kamadeva (Manmadha) to ashes?
What is the story behind it?
The story of Lord Shiva burning Kamadeva to ashes is related to Shiva's marriage with Parvati Or Girija and birth of Kartikeya for killing of poweful demon Tarakasura .It was plan of all the gods.
Since the death of sati Shiva's wife (previous) , in grief ,he was retreated to the Himalayas and was engaged deep in penance. Meantime gods were unable to fight Tarakasura, all they went to Lord Brahma . And he told them that only Lord Shiva’s child is powerful enough to kill the Tarakasura he adviced them to pray to Adi-Shakti / Mahadevi (goddess) , goddess then reappeared before them and assured them that she would reincarnate as Parvati , the daughter of Himalayas. Thus goddess Parvati was born. She expressed her desire to marry lord Shiva went near lord shiva. Seeing Shiva is not affected by Parvati's charm Brahaspati spokes about deploying Kamdeva for disturbing his penance to unite both. Kamdeva thus went near Lord Shiva and shot arrows of love at him . When Shiva was affected by his arrows , he was surprised and angirely looked at Kamdeva with his third eye . And due to power of Shivas third eye the Kamdeva instantly got burned into ashes.
The story is also found in Skanda Purana - Part 1 - Chapter 21 - parvati's Penance -
बृहस्पतिरुवाचेदं महेंद्रं प्रति सद्वचः॥
एवमेतत्त्वया कार्यं महेंद्र श्रूयतां तदा॥ 21.36 ॥
एतत्कार्यं मदनेनैव राजन्नान्यः समर्थो भविता त्रिलोके॥
विप्लावितं तापसानां तपो हि तस्मात्त्वरात्प्रार्थनीयो हि मारः॥ 21.37 ॥
36-37. Brahaspati spoke the following good words ( of advice) to Mahendra : " O Mahendra , this must be done by you. Let it be heard . This task can be carried out only by Madana (the god of love) o king. None else will be competent for it in all three worlds.The penance of many ascetics has been upset by him. Hence Mara (god of love) should be requested (in this matter) immediately .
॥देवा ऊचुः॥ मदनद्वं समर्थोसि अस्माञ्जेतुं सदैव हि॥
महेशं प्रति गच्छाशु सुरकार्यार्थसिद्धये॥
पार्वत्या सहितं शंभुं कुरुष्वाद्य महामते॥ 21.46 ॥
Devas said O Madana , you are capable of always conquering us. (But) go immediately to Mahesa for accomplishing the task of Suras . Unite Shambhu with Parvati , O highly intelligent one.
एतस्मिन्नंतरे तत्र मदनो हि धनुर्द्धरः॥
पंचबाणान्समारोप्य स्वकीये धनुषि द्विजाः॥
तरोश्छायां समाश्रित्य देवदारुगतां तदा॥ 21.59॥
In the mean time Madana took up his bow and fixed five arrows to it .O Brahmanas he resorted to the shade of Deva-Daru tree.
तावद्विद्धः शरेणैव मोहनाख्येन चत्वरात्॥
विध्यमानस्तदा शंभुः शनैरुन्मील्य लोचने॥
ददर्श गिरिजां देवोब्धिर्यथा शशिनः कलाम्॥ 21.64 ॥
At the time Shambhu was hit and pierced with the arrow called Mohana ( the Ennchanter) suddenly . On being hit shambhu opened his eyes slowely . The Lord saw Girija like the ocean viewing the digit of the moon.
तां निरीक्ष्य भवो देवो गिरिजां लोकपावनीम्॥
मुमोह दर्शनात्तस्या मदनेनातुरीकृतः॥
विस्मयोत्फुल्लनयनो बभूव सहसा शिवः॥ 21.68 ॥
On seeing Girija , the sanctifier of all the worlds, lord Bhava became fascinated .At her site he was affected by Madana. Siva's eyes suddenly became expanded due to surprise.
Then the Shiva thought to himself ,I was engaged in penance , I am devoid of blemishes . yet how I was enchanted by this girl?
ततो व्यलोकयच्छंभुर्द्दिक्षु सर्वासु सादरम्॥
तावद्दृष्टो दक्षिणस्यां दिशि ह्यात्तशरासनः॥ 21.71 ॥
चक्रीकृतधनुः सज्जं चक्रे बेद्धुं सदाशिवम्॥
यावत्पुनः संधयति मदनो मदनांतकम्॥
तावद्दृष्टो महेशेन सरोषेण तदा द्विजाः॥ 21.72॥
Then Shambhu looked in all directions earnestly . Madana was seen by him in the south with the bow lifted up. The god of love bented his bow like a circle. ,kept it ready ,drawn in order to pierce and wound Sadashiva .But by the time he was able to discharge the arrow , O Brahmanas.
निरीक्षितस्तृतीयेन चक्षुषा परमेण हि॥
हाहाकारो महानासीद्देवानां तत्र पश्यताम्॥ 21.73 ॥
He was looked at with the third eye by the greatest lord . **Madana was instantly encircled by clusters of flames .**There was a loud wailing among devas who stood there watching.
We can read the full story in the subsequent chapters through the link.
Lord Brahma told Narada that the deities decided to send Kamadeva to influence lord Shiva so that the marriage between him and Parvati is felicitated.
Indra called Kamadeva and told him that the demon king Tarakasur could be killed only by such a person who was the son of Shiva and Parvati. Indra instructed Kamadeva to arouse passion in lord Shiva, so that he agrees to marry Parvati.
Kamadeva, accompanied by his wife Rati went to lord Shiva to accomplish his mission.
After reaching the place where lord Shiva was engrossed in his meditation, Kamadeva made repeated attempts to arouse passion in the heart of lord Shiva, but his actions were no avail.
Right then, Kamadeva saw Parvati arriving accompanied by her companions. She was looking divine in her beauty. Just at that moment lord Shiva too had come out of his meditational trance. Kamadeva thought that it was the most appropriate moment to have a go.
Kamadeva struck lord Shiva with his 'Kamabana' which did have a deep impact on him. Lord Shiva was struck by the awesome beauty of Parvati and his heart became full of passion for her. But at the same time he was surprised at the sudden change in his behaviour. He realized that it was an act of Kamadeva.
Lord Shiva looked all around him. He saw Kamadeva standing towards his left side, with a bow and arrows in his hands. Now he was fully convinceed that it was indeed an act of Kamadeva.
Kamadeva became terrified, he started remembering god, but before the deities could come at his rescue the third eye of lord Shiva got opened and Kamadeva was reduced to ashes.
Parvati got scarred after seeing Lord Shiva in such a destructive anger. She went to her house along with her companions. Rati- the wife of Kamadeva wept unconsolably.
The deities arrived and consoled her by saying that by the grace of lord Shiva, her husband would be alive once again. After that the deities went near lord Shiva and did his worship. They told him that it was not the fault of Kamadeva, as he had acted in accordance with the aspirations of the deities. They also told him the mystery of Tarakasur's death. The deities then requested him to make Kamadeva alive once again.
Lord Shiva told the deities that Kamadeva would take birth as the son of Krishna and Rukmini in the era of dwapar. A demon by the name of Shambar would throw him off in the sea. He would kill that demon and marry Rati, who too would be living in a city near the sea.