> Kurma, the second incarnation of Vishnu came about at a time when the devas (gods) and asuras (demons) were constantly fighting. At one point, the asuras became very powerful and Vishnu advised the devas to churn the ocean so that amrita, the nectar of immortality would rise to the surface. The mountain Mandara was used to churn the ocean and Vishnu incarnated as the tortoise, Kurma, using his hard shell as a base to support the mountain.
> Sukadev Goswami continued: In Hiranmaya-varsa, the Supreme Lord, Visnu, lives in the form of a tortoise [kurma-sarira]. This most dear and beautiful form is always worshiped there in devotional service by Aryama, the chief resident of Hiranmaya, along with the other inhabitants of that land.
O my Lord, I offer my respectful obeisances unto You, who have assumed the form of a tortoise. You are the reservoir of all transcendental qualities, and being entirely untinged by matter, You are perfectly situated in pure goodness. You move here and there in the water, but no one can discern Your position. Therefore I offer my respectful obeisances unto You. Because of Your transcendental position, You are not limited by past, present and future. You are present everywhere as the shelter of all things, and therefore I offer my respectful obeisances unto You again and again.
> At times we alleviate an itching sensation by blowing upon it. Similarly, Srila Bhaktisiddhanta Sarasvati Thakura explains that the breathing of the Supreme Personality of Godhead can alleviate the itching sensation within the minds of mental speculators, as well as the itching of the material senses of conditioned souls engaged in sense gratification. Thus by meditating on the windy breath of Lord Kurma—the tortoise incarnation—all categories of conditioned souls can be relieved of the deficiencies of material existence and come to the liberated, spiritual platform. One must simply allow the pastimes of Lord Kürma to blow within one’s heart like a favorable breeze; then one will surely find spiritual peace.
MORE EXPLANATION:
Further to Pralaya- deluge at the beginning of the present Kalpa the Gods (devas) lost their immortality due to a curse by the short-tempered sage Durvasa.The sage had once presented a garland of flowers to Indra,king of gods, who carelessly gave it away to his elephant which trampled it. The Devas approached Vishnu for help. Vishnu then asked them to churn the ocean of milk after adding medicines into the ocean. Mt Mandara could be used a the churning stick he said. He requested them to ask them help of Asuras in lifting the mountain in exchange for offer of the share of nectar of immortality that would ensue from the churning.
Both the devas and the asuras churned the ocean using the serpent Vasuki as the rope. At the start, playing a Machiavellian trick, Indra, king of the gods asked the asuras for the head end of vasuki. But asuras suspecting foul play, took the head end, only to be deceived as the poison from Vasuki was slowly weakening them. But as churning was proceeding the mountain was sinking and then Lord Vishnu took the form of the tortoise KURMA and kept the mountain afloat. As soon as the bowl of amrita, the nectar of immortality was out, the asuras grabbed it. Then Lord Vishnu took the form of an apsara, a beautiful maiden, and seduced the asuras into letting her distribute the nectar and also to abide by her order of distribution. As soon as the devas were served the maiden disappeared thus totally deceiving the asuras and making them totally weak.