The story associated with the reason for performing Samudra Manthan, or churning of ocean, is associated with Sage Durvasa. This story is found in the Vishnu Purana.
Sage Durvasa once received a flower garland which had a unique fragrance. While roaming through the forest with the garland, Durvasa came across Lord Indra (king of demigods) who was sitting atop his white elephant Airavat. The Sage gifted the garland to Lord Indra and he placed it on the head of Airavat.
Airavat wanted to know the reason for the unique fragrance and using his trunk he tried to get the garland. But unfortunately the garland fell down and the elephant stamped on it.
Durvasa happened to see this and he thought it was done purposefully to insult him. He thought that Indra has gone arrogant with wealth, power and prosperity.
Durvasa cursed Indra to become pauper.
The curse proved to be fatal and Indra lost all his glory. The Devas thought that the Asuras will take advantage of their precarious situation and would drive them out of heaven.
The Devas then approached Lord Vishnu for help. He said that Goddess Lakshmi has disappeared deep into the oceans and the only way to make her reappear was by Samdura Manthan or Churning of the Ocean.