Kurma avatar belongs to the Satya Yuga and in this avatara Mahavishnu incarnated as a giant turtle to save the earth from destruction. Kurma Avatar of dashavatar is explained mainly in the Bhagavad Purana, Agni Purana and Ramayana. Kurma Purana, one of the major eighteen Puranas, is said to have been directly stated by Lord Vishnu to the sage Narada, and it contains the details about the Kurma avatar.
The second avatar of Dashavatara is Kurma avatar. Kurma means tortoise. Vishnu took the form of turtle to help devas and asuras ( gods and demons). They were churning ocean to receive the gifts from the ocean. Lord VIshnu helped the devas in two counts. First, he acted as base to support the Mount Mandar, which was used as an axis for churning of ocean. Second, as Mohini to take hold of nectar (or amrit). Due to this gods got an upper hand in “Dev Asur sangharsh”.
Durvasa curse to Indra
Devas grew weaker due to a curse of Sage Durvasa. The demons or asuras, a group of malicious deities in the Hindu mythology, tried to overcome them. A war followed, which continued for long. Despite fighting bravely, devas could not win over the asuras. They asked Lord Vishnu for help.
Advice of Lord Vishnu
Lord Vishnu asked the devas to use Mount Mandara as a churning stick. But, they could not pull up the mountain. On advice of Lord Vishnu, the gods and asuras made a deal to churn the ocean jointly. They pulled the Mount Mandara and used it as a churning stick. Serpent Vasuki was used as a rope. it was pulled first one way and then the other. During churning, Mandara began to sink into the mud at the bottom of the milk ocean. Vishnu took the form of Kurma (second dashavatara), and held the mountain on his broad back.
As a result of the churning, amrita was obtained which asuras took control of it. Here Vishnu, took the form of a beautiful lady, Mohini. He managed to take the nectar bowl with him and gave it to devas. Thus devas eventually got powerful. Thus, Vishnu helped them once again and as Kurma Avatar.