Kurma (or the Koorm Avatar) is the second, turtoise-incarnation of Lord Vishnu.
At the Churning of the Ocean, the Mount Mandara that was used as a churning stick, began to sink into the soft ocean bed. This caused Vishnu to assume the form of the turtoise-avatar, diving to the bottom where his back became a pivot for the churning stick.
The Kurma incarnation also represents the stage in the development of life, when the ability to breathe air and walk out of the water developed. The turtle is also the symbol of perseverance.