Samudra-manthan is the churning of the Ocean of Milk. Here is the exact story of it in an article on Wikipedia for Samudra Manthan:-
According to this the story for Samudra-Manthan is as such:-
Indra, the King of heaven, while riding on the elephant Airavata, came across Sage Durvasa who offered him a special garland given to him by Lord Shiva. Indra accepted the garland and placed it on the trunk of the elephant as a test to prove that he was not an egoistic god. The elephant, knowing that Indra had no control over his own ego, threw the garland to the ground. This enraged the sage as the garland was a dwelling of Sri (fortune) and was to be treated as a prasada or religious offering. Durvasa cursed Indra and all devas to be bereft of all strength, energy, and fortune.
In battles following the incident, the Devas were defeated and Asuras (demons) led by Bali, gained control of the universe. Devas sought help from the Supreme God Vishnu who advised them to treat asuras in a diplomatic manner. Devas formed an alliance with asuras to jointly churn the ocean for the nectar of immortality and to share it among them. However, Vishnu told the Devas that he would arrange for them alone to obtain the nectar.
The churning of the Ocean of Milk was an elaborate process. Mount Mandara was used as the churning rod, and Vasuki, the king of serpents, who abides on Shiva's neck, became the churning rope. The demons demanded to hold the head of the snake, while the gods, taking advice from Vishnu, agreed to hold its tail. As a result, the demons were poisoned by fumes emitted by Vasuki. Despite this, the gods and demons pulled back and forth on the snake's body alternately, causing the mountain to rotate, which in turn churned the ocean. When the mountain was placed on the ocean, it began to sink. Vishnu, in the form of a turtle Kurma, came to their rescue and supported the mountain on his back.
The Samudra Manthana process released a number of things from the Ocean of Milk. One was the lethal poison known as Halahala, which in some versions of the story, escaped from the mouth of the serpent king as the demons and gods churned. This terrified the gods and demons because the poison was so powerful that it could destroy all of creation. Then the gods approached Shiva for protection. Shiva consumed the poison in an act to protect the universe, and his consort, Parvati, grabbed Shiva's throat in an effort to prevent the most deadly poison from affecting the universes inside Lord Shiva. As a result, Shiva's throat turned blue. For this reason, Lord Shiva is also called Neelakantha (the blue-throated one; "neela" = "blue", "kantha" = "throat" in Sanskrit).
The Ocean of Milk is not our normal ocean but is one of the seven oceans and also called as Kshir Sagar
In Hindu cosmology, the Ocean of milk (kṣīroda, kṣīrābdhi or Kṣīra Sāgara) is the fifth from the center of the seven oceans. It surrounds the continent known as Krauncha.
Here is an article for info on Seven Oceans in Hindu Mythology