During Pradosha timings 4:30 to 6 PM on Trayodasi thithi, in case of vaishnavites why Lord Narasimha is worshipped and what is the significance of this?
The legend of Narasimham and Prahalad goes like this,
Hiranyakashipu asks for a tricky boon. That he would not die either on earth or in space; nor in fire nor in water; neither during day nor at night; neither inside nor outside (of a home); nor by a human, animal or God; neither by inanimate nor by animate being.
Brahma grants the boon. With virtually no fear of death he unleashes terror... (SB 7.3.35-38)
Prahlada, Hiranyakashipu's son who is a stauch Vishnu devotee declares the omnipresence of Lord Vishnu and refuses to worship his own father as the Lord of the world.
Once Hiranyakashipu points to a pillar and asks if Vishnu is present in it. Prahlada nods in affirmative. Angered at it, he draws his sword and cuts the pillar; Narasimha appears out of the broken pillar.
Narasimha (being a man-lion god form) kills Hiranyakashipu. He comes out to kill at the pradosha or twilight (neither day nor night);on the doorsteps of his palace (neither inside nor outside); uses his nails to kill (neither animate nor inanimate); puts him on his lap before killing (neither earth nor in space). Thus making power of the boon ineffective. (SB 7.8)
Thus, pradosha is the time when Narasimha completed his principal objective of his avatara and thus rescused Prahalada. Vishnu devotees observe silence or mauna during the period. No mantras are recited during the period either.
Though the answer above is correct but as it is required here to quote from specific Purana, so I am quoting from Narsingh Purana which is considered to be Uppurana.
The story is mentioned in Narsingh Purana Chapter 44.
तावद्धता युद्ध्यमाना दैत्याः कोटिसहस्त्रशः।
नरसिंहेन यावच्च नभोभागं गतो रविःः।।२७
Until sun is not set (gone to west), lord Narsingh was fighting with lacs and crores of demons.
शस्त्रास्त्रवर्षचतुरं हिरण्यकशिपुं जवात्।
प्रगृहृं तु बलाद्राजन् नरसिंहो महाबलः।।२८
But when sun is about to set, the almighty Narsingh has forcefully grabbed the knower of all weapons Hiranyakashipu.
संंध्याकाले गृहद्वारि स्थित्वारी स्थाप्य तं रिपुम्।
वज्रतुल्यमहोरस्कं हिरण्यकशिपुं रुषा।
नखैः किसलयमिव दारयत्याह सोसुरः।।२९
Then at the time of evening at the door lord Narsingh plunked down Hiranyakashipu on his thigh and started tearing him by his nails.
Note- I have sanskrit and hindi version of this book. The english translation is written by me. So, if anyone got any issue please suggest.
Found this in indiadevine site (http://www.indiadivine.org/content/topic/980214-krishnanarayanalord-siva/?do=findComment&comment=5784716) Wish to share the same.
Narasimha is Narayana and Sadashiva
Problem is that many people hasn't understood "Narasimhadeva". Narasimhadeva has no beginning or end. He is Original "Narayana". He is source of all avatars. He is source of heat of the sun and keeping cool laxmi maa (parashakti) on his chest/lap. He has nine planets in his divine face. All panch buthas are at his feet. All gods do their job by his fear or bakthi towards him.
He is keeping yoga-maya as his illusinory energy. He is the aadi omkara jwala. He is Narayana. All mantras, tantras, sastras, weapons come from him and surrender within him. He generated Maha-Sudarshana Chakra from it all gods got their weapons. He controls the time thru his kala-chakra. (behind every sudarsha chakra shrine you can see narasimha sitting). He ends everything thru his third eye at end of kalpa. At that time he himself is Sada-shiva or mahaa-kalaa. For Vaishnavas he gives his divine darshan thru his divine Vasudeva form. For Shaivas [rudras followers (not pseudo-shaivas)] or Siddas or Rishis he gives watever powers they ask by giving darshan in form of divine aadi-jyoti. They worship him in form of Linga. He is the one who resides within each linga. Rudra represents our body. Linga represents our aatma. Inside our aatma "narasimha" resides as aatma-jyothi. In all shiva temples you can see rudra outside as urchava, since hes outside the linga. Inside linga it is "Narasimha - the param jyoti" residing. Whenever siddhas enjoy bliss of this jyoti they dance with joy. Since this dance is divine, this dance is taken as form of worship. Rudra being a chief of all siddhas dances in this way so hes called nataraja. Dance is called bharatanatyam. During shivarathri siddhas (including rudra) realises this parama-jyoti. So special Worship is done at siddha pittas, rudra temples and shiva-lingas as parama-jyoti is residing inside the linga (aatma).
The above truth is beautifully illustrated by Madhvacharya. Shivarathri are celebreated by Madhvas also. Pradhosam is celebreated in all great Narasimha temples.
At Pradosham time Narashima give's darshan to everyone. At this time he accepts all prayers of devas, rudra, brahma and gurus. So at pradosham time, in shiva temples only nandi is collecting prayer from us as rudra is busy in worshippine narasimha (eventhough shaivatees will say something reverse). When Rudra tells in his Gita that Sada-Siva is supreme, he is actually referring Narayana(Narasimha). Since Gita told by Rudra (in padma purana) may create confusion, all acharyas took "Bhagavath Gita" told by Lord Krishna (narasimha himself) as authorotative. Read Narasimha Upanishads, Narashima Sahasranama and Narasihma Purana. There everything explained clearly. Also Read Sri Vedantha Desikars commentary about Narasimhadeva. he clearly explains above. Also Nammalwar told It is Narasimha residing everywhere. Even in Vishnu Sahasranama it is Narasimha pointed out at many times. It is narasimha praised as Sadashiva in "shiva sahasranama". All Gods have praised stotras in praise of Narashima. Even Narasimhas own avatars have worshiped and praised Narasimhadeva. So whenever someone tells Rama/krishna worshipped linga then it should be understood that they worshiiped Narasimha thru linga. Worshpiing Narasimha in form of linga is very ancient method as its easy to make a linga than sculpting his divine form. Only after people gained mastery over crafts they started sculpting narasimha and his divine forms. Both Madhvacharya and Vedantha desikar had told that when narasimha killed hiranyakashipu, blood of hiranya was consumed by narasimadeva to wash off his sins(as requested by prahlada alwar), [in narasimha temples panaga representing blood is given as prasada to narasimhadeva]. hiranyas hide(skin) was worn by virabadra, hiranyas head is accepted by Kaalidevi, hiranyas soul is given to saraba(death ie., rudra) who made sure that this aatma will born again according to its karma. Even death(saraba) is controlled by Narasimha only.
Narsimhadeva's anger was calmed down by Prahladalwar's prayers (as God stoops down to devotees pure prayers, he cant be controlled thru ahankara). But shivapurana being tamasic it illustrates everything as reverse just as kaali devotees wrongly tell as though kaali defeated rudra (but actually rudra defeated kaali). It is Narasimhadeva standing in his divine form as "Venkateswara" in Tirumala as to his devotees as he always gives darshan thru his divine Vasudeva form. Since Vaishnavas are soft-hearted Narasimha always gives darshan in form of divine Vasudeva form. Thats why worshiping Narasimha in form of Vasudeva, Rama, krishna is much more prevalent than form of Narasimha himself. Om Namo Narayanaya.