Kurma Avatara is one among the ten incarnations of Lord Vishnu (Dashavatara). Kurma is a sanskrit word which means Tortoise. Tortoise is known for its stability and introspective nature.
Here is the story of the Kurma Avatara
Once on the advice of lord Vishnu to get Amrutham (the divine nectar) gods plan to churn the Ksheerasgara (ocean of milk). But their strength was not sufficient and again with the advise of Vishnu, they ask demons for help and in return offer them a share in the Nectar. The demons readily agree. Gods and demons started churning Ksheera sagara (ocean of milk) for Amrutham (the drink that is considered to cause immortality). They use Mandhara mountain as the Pole and Vasuki, the snake as the rope for churning. Before they start, the fight comes as to who has to catch the head of Vasuki and the tail of Vasuki. On advice of Vishnu the Gods say that they would hold the head and the demons get into their egoistic self and say that they are more superior and will not catch the end or tail. The gods readily agree and catch the tail and demons the head. As they churn, Vasuki emits a lot of poison and the demons are hurt. They understand that the gods have tricked them, but because it was their choice they had no other alternative and in lure of Amrutham, they continued churning.
As they churn a lot of things come significant being Godess Lakshmi who was given to Lord Vishnu, Kaamdhenu the divine cow etc and also Halahala (the poison) that was take by Lord Shiva. Before they could actually get Amrutham the mountain starts to slip inside the Ksheerasagar and so were unable to continue churning. All of them pray lord Vishnu, then he takes the form of a big tortoise and holds the mountain on his back until the Amrutham is obtained.
By taking this form God has sent the message to the devotees that even if you are being burdened by mountains of pressure, lured by all the worldly pressure one should be steady and his aim must only to be to reach the lord. Tortoise pulls all its body parts inside and is steady, similarly the devotee should push aside all the bodily pleasures and must not be moved.