Tarakasura had a boon that he can be killed only by Shiva s son. Lord Shiva and Goddess Parvati’s son Kartika was called by his parents and was asked to destroy the Asur. Kartika was also named Subrahmanya, Muruga and Skanda.
Lord Muruga took the blessings of his parents and set off to destroy the demon. He carried a dozen weapons with him, eleven of which were given by his father Lord Shiva and the Vel (spear) given by his mother Parvati. Lord Muruga destroyed Tharakasuran on the Poosam Nakshatra day in the Tamil month of Thai and hence Thai Poosam is celebrated in all Murugan temples.
Another legend says, when Shiva was passing on a mantra to Parvati, Lord Muruga eavesdropped on them. Parvati got annoyed by this and cursed him. To save himself from the curse, Lord Muruga offered hard sacrament at Thiruparankundram.
Parvati got pleased with his penance, Shiva and Parvati appeared before him and relieved him from the curse. The day on which the curse was removed is Thai Poosam.
It is thus a special day on which Lord Muruga or Subrahmanya is worshipped and is celebrated in a very splendid manner at all Murugan temples.
Another legend about Thaipoosam is associated with the Kavadi. It involves Lord Muruga testing the determination of Idumban, the student of Sage Agasthya.
According to another legend Lord Shiva and Parvati were involved in a celestial dance on the Thaipusam day. It is said that all the gods assembled to watch this cosmic dance.
According to another myth, River Kaveri was jealous of River Ganga because of getting so much of importance - especially with Ganga getting a place in the veil of Lord Shiva. She prayed to Lord Vishnu and it is believed that Lord Vishnu appeared before her on Thaipoosam day.