The primeval Lord then assumed the tortoise incarnation in order to serve as a resting place (pivot) for the Mandara Mountain, which was acting as a churning rod. The demigods and demons were churning the ocean of milk with the Mandara Mountain in order to extract nectar. The mountain moved back and forth, scratching the back of Lord Tortoise, who, while partially sleeping, was experiencing an itching sensation.
(Srimad Bhagavatam------2:7:13------translation).

The gigantic work of churning the milk ocean by the combined effort of the demigods and the demons required a gigantic resting ground or pivot for the gigantic Mandara Hill. Thus to help the attempt of the demigods the primeval Lord assumed the incarnation of a gigantic tortoise, swimming in the ocean of milk. At the same time, the mountain scratched His backbone as He was partially sleeping and thus relieved His itching sensation.
(Srimad Bhagavatam------2:7:13------purport).

Some of the arcā representations of the Lord situated in different places of pilgrimage are mentioned herewith. The Lord is present at Mathurā (the birthplace of Lord Kṛṣṇa) as Ādi-keśava; the Lord is present at Purī (Orissa) as Lord Jagannātha (also known as Puruṣottama); He is present at Allahabad (Prayāga) as Bindu-mādhava; at Mandara Hill He is present as Madhusūdana. In the Ānandāraṇya, He is known as Vāsudeva, Padmanābha and Janārdana; at Viṣṇukāñcī, He is known as Viṣṇu; and at Māyāpura, He is known as Hari. There are millions and billions of such arcā forms of the Lord distributed all over the universe.
(Srimad Bhagavatam------3:1:17------purport).

The yogī should further meditate upon the Lord's four arms, which are the source of all the powers of the demigods who control the various functions of material nature. Then the yogi should concentrate on the polished ornaments, which were burnished by Mount Mandara as it revolved. He should also duly contemplate the Lord's discus, the Sudarśana cakra, which contains one thousand spokes and a dazzling luster, as well as the conch, which looks like a swan in His lotuslike palm.
(Srimad Bhagavatam------3:28:27------translation).

All departments of law and order emanate from the arms of the Supreme Personality of Godhead. The law and order of the universe is directed by different demigods, and it is here said to emanate from the Lord's arms. Mandara Hill is mentioned here because when the ocean was churned by the demons on one side and the demigods on the other, Mandara Hill was taken as the churning rod. The Lord in His tortoise incarnation became the pivot for the churning rod, and thus His ornaments were polished by the turning ofMandara Hill. In other words, the ornaments on the arms of the Lord are as brilliant and lustrous as if they had been polished very recently.
(Srimad Bhagavatam------3:28:27------purport).

Once Mahārāja Āgnīdhra desired to have a son, and therefore he entered a cave of Mandara Mountain to practice austerity. Understanding his desire, Lord Brahmā sent a celestial girl named Pūrvacitti to Āgnīdhra's hermitage. After dressing herself very attractively, she presented herself before him with various feminine movements, and Āgnīdhra was naturally attracted to her. The girl's actions, expressions, smile, sweet words and moving eyes were fascinating to him. Āgnīdhra was expert in flattery. Thus he attracted the celestial girl, who was pleased to accept him as her husband because of his mellifluous words. She enjoyed royal happiness with Āgnīdhra for many years before returning to her abode in the heavenly planets.
(Srimad Bhagavatam------5:2------summary).

On the lower slopes of Mandara Mountain is a mango tree named Devacūta. It is 1,100 yojanas high. Mangoes as big as mountain peaks and as sweet as nectar fall from the top of this tree for the enjoyment of the denizens of heaven.
(Srimad Bhagavatam------5:16:16------translation).

Hiraṇyakaśipu wanted to become immortal. He wanted not to be conquered by anyone, not to be attacked by old age and disease, and not to be harassed by any opponent. Thus he wanted to become the absolute ruler of the entire universe. With this desire, he entered the valley of Mandara Mountain and began practicing a severe type of austerity and meditation.
(Srimad Bhagavatam------7:3------summary).

The wife of Vairāja, whose name was Devasambhūti, gave birth to Ajita, an incarnation of the Supreme Personality of Godhead. This Ajita, taking the shape of a tortoise and holding the mountain known as Mandara on His back, churned the ocean and produced nectar for the demigods.
(Srimad Bhagavatam------8:5------summary).

By churning the ocean of milk, Ajita produced nectar for the demigods. In the form of a tortoise, He moved here and there, carrying on His back the great mountain known as Mandara.
(Srimad Bhagavatam------8:5:10-------translation).

The Supreme Personality of Godhead, who is known as Ajita, unconquerable, advised the demigods to make a peace proposal to the demons, so that after formulating a truce, the demigods and demons could churn the ocean of milk. The rope would be the biggest serpent, known as Vāsuki, and the churning rod would be Mandara Mountain. Poison would also be produced from the churning, but it would be taken by Lord Śiva, and so there would be no need to fear it.
(Srimad Bhagavatam------8:6------summary).

Following the instructions of the Supreme Personality of Godhead, the demigods established a peace with Mahārāja Bali, the King of the demons. Then both the demons and the demigods started for the ocean, taking Mandara Mountain with them. Because of the great heaviness of the mountain, the demigods and demons became fatigued, and some of them actually died. Then the Supreme Personality of Godhead, Viṣṇu, appeared there on the back of His carrier, Garuḍa, and by His mercy He brought these demigods and demons back to life. The Lord then lifted the mountain with one of His hands and placed it on the back of Garuḍa. The Lord sat on the mountain and was carried to the spot of the churning by Garuḍa, who placed the mountain in the middle of the sea. Then the Lord asked Garuḍa to leave that place because as long as Garuḍa was present, Vāsuki could not come there.
(Srimad Bhagavatam------8:6------summary).

O demigods, cast into the ocean of milk all kinds of vegetables, grass, creepers and drugs. Then, with My help, making Mandara Mountainthe churning rod and Vāsuki the rope for churning, churn the ocean of milk with undiverted attention. Thus the demons will be engaged in labor, but you, the demigods, will gain the actual result, the nectar produced from the ocean.
(Srimad Bhagavatam------8:6:22-23------translation).

Vāsuki, being a great snake, would be natural food for Garuḍa, the chief of birds. Lord Viṣṇu therefore asked Garuḍa to leave so that Vāsuki could be brought to churn the ocean with Mandara Mountain, which was to be used as the churning rod. These are the wonderful arrangements of the Supreme Personality of Godhead. Nothing takes place by accident. Carrying Mandara Mountain on the back of a bird and putting it in its right position might be difficult for anyone, whether demigod or demon, but for the Supreme Personality of Godhead everything is possible, as shown by this pastime.
(Srimad Bhagavatam------8:6:39-------purport).

By the expert arrangement of the Supreme Personality of Godhead, the demons held the snake near the mouth, whereas the demigods held the tail of the great snake. Then, with great endeavor, they began pulling the snake in both directions. Because the churning rod, Mandara Mountain, was very heavy and was not held by any support in the water, it sank into the ocean, and in this way the prowess of both the demons and the demigods was vanquished. The Supreme Personality of Godhead then appeared in the form of a tortoise and supported Mandara Mountain on His back. Then the churning resumed with great force.
(Srimad Bhagavatam------8:7------summary).

Everyone in this material world is under the different modes of material nature. There were three different parties in the churning of Mandara Mountain—the demigods, who were in the mode of goodness, the demons, who were in the mode of passion, and the snake Vāsuki, who was in the mode of ignorance. Since they were all becoming tired (Vāsuki so much so that he was almost going to die), Lord Viṣṇu, to encourage them to continue the work of churning the ocean, entered into them according to their respective modes of nature—goodness, passion and ignorance.
(Srimad Bhagavatam------8:7:11-------purport).