Kurma Jayanti is observed on the day of Purnima in the month of Vaishakh. It is said that Lord Vishnu incarnated as Kurma (Turtle) on this day and he lifted Mandaranchal parvat on his back in this incarnation as Kurma.
Legend behind Kurma Avatar :
Lord Vishnu can be seen as a turtle in this incarnation which has been related to Samudra Manthan, i.e, the battle between Devas and Demons that happened in the sea. It is said that during the reign of Bali, the demons were very robust and they also had the strengh of Shukracharya.
Devas were unable to battle with them as Lord Indra was cursed by Saint Durvasa and was inadequate. Taking benefit, Bali established his realm in all three lokas and devas were wandering weak
All devas together went to Lord Brahma and asked for assistance. Lord Brahma along with all devas, visited Lord Vishnu and told him about the problem. Lord Vishnu suggested about the battle which would take place in Kshir Sagar. During this battle, devas would consume Amrit (Holy water). They would be immortal and would be able to kill the demons.
Devas agreed for the battle as suggested by Lord Vishnu. They chose Mandaranchal parvat as the centre and Nagraj Vasuki as the rope. They took the Mandaranchal parvat to Kshir Sagar but it started drowning as soon as it was left there.
During this time, Lord Vishnu incarnated as Kurma and lifted Mandaranchal parvat on his back. Thus, the battle between the Devas and the Demons could be completed.
Significance of Kurma Jayanti :
This day is considered to be very significant according to the Shastras. Starting construction works on this day is considered to be very auspicious as it is believed that Yogmaya resides with Kurma. This day is also auspicious for works related to Vastu, shifting in a new house etc.
Rituals of Kurma Jayanti :
Devotees keep fasts from the night before to the day after. They offer worship to Lord Vishnu. Staying awake at night and reciting Vishnu Sahasranama is very auspicious. Donating food to Brahmans is considered propitious.