Kurma Avatara is the second Avatara of Lord Vishnu. The story of Kurma Avatara is also mentioned in Padma Purana’s Uttara Khanda.
Once, goddess Parvati expressed her desire to know about all the incarnations of Lord Vishnu.
Lord Mahadeva replied —
Durvasa was the son of Sage Atri. Once, he went to Indraloka to see Indra. At that time, Indra was planning to go out somewhere. Durvasa presented a garland of Parijat flowers to Indra. Indra, after receiving the garland from Durvasa kept it carelessly on the forehead of his elephant-Airavat. This garland was trampled under its feet by the elephant, which infuriated Durvasa. He cursed Indra by saying—Immense prosperity has made you arrogant. But you will become a pauper within a very short time.
Durvasa’s words came to be true and Indra found that not only the heaven but all the three worlds had become bereft of goddess Lakshmi. Prosperity vanished and poverty prevailed everywhere. The deities became worried and went to take the help of Brahma. Brahma took the deities to Lord Vishnu. Vishnu became pleased with their eulogy and said —
I will take incarnation as Kurma. If the ocean were churned with the help of Mandarachal mountain and Vasuki, then goddess Lakshmi would manifest herself. I shall hold the Mandarachal mountain on my back. This way the churning of ocean commenced. The Mandarachal mountain was uprooted and placed inside the ‘Ksheer-Sagar’ and which rested on the back of Lord Kurma. The serpent–Vasuki, was held by deities and demons on both the ends. First of all the most venomous poison–Kalkut emerged from the ocean. Seeing both the deities and demons unwilling to accept it. (Lord Shiva) drank it.
After the emergence of Kalkut, goddess Daridra and Varunai manifested themselves. Similarly, Airavat- elephant, Uchchaishrava-horse, Dhanvantari, Surabhi–cow and Parijat- tree emerged from the ocean. Ultimately, goddess Lakshmi manifested herself. The deities requested her to dwell in the heart of Lord Vishnu and bless all the three worlds by her presence. Goddess Lakshmi agreed and blessed them.