Kurma Jayanti is the appearance day of Lord Kurma, the second incarnation of Lord Vishnu. The Supreme Lord appeared as a giant tortoise to help the Devas (gods) and Asuras (demons) during the churning of the ocean of milk, also known as Samudra Manthan.
In this divine form, Lord Kurma provided the stable base on which Mount Mandara rested, allowing the churning to continue and ultimately leading to the emergence of the nectar of immortality (amrita).