Kurma Avatara is the second avatar in Dashavataras of Lord Vishnu in which he incarnates himself as a tortoise.
The story of why Lord Vishnu took this form is very interesting, Sura and Asuras i.e., gods and demons had a constant fight between them to prove who is more powerful, once all gods lost their powers due to a curse by short tempered Sage named Durvasa.
Durvasa presented a garland of immense power to the king of gods Indra once but Indra being negligent gave it to his elephant Iravath which trampled the garland causing Durvasa anger and he cursed all gods to lose power. Losing their power gods were weak and chased by demons, ran to Lord Vishnu to save them.
Lord Vishnu advised gods to churn the ocean milk “Kshir Sagar” to extract Amrit “elixir” which drinking which will make gods immortal. Churning the ocean is not an easy task even for gods so they invited demons too for the event, Vasuki the mighty snake took the role of being used as rope and mount Mandara as the staff.
When gods n demons started churning milk mount Mandara would not hold and sink as there was no base to stand as the ocean was too deep to its size so when all gods prayed to Lord Vishnu he took the form of “Kurma” the tortoise and stood under mount Mandara and then churning was possible.
Demons were lured into churning by promising Amrit to them but asuras suspecting gods chose to hold the head of Vasuki during churning little they knew that Vasuki’s poison from the head would weaken them.
When Amrit in a bowl appeared asuras grabbed it then lord Vishnu had to take the form of an apsara named Mohini and deceived demons to serve Amrit to gods.