What occurs when a senator delays the vote by talking it to death?

A "filibuster" is a procedure by which a senator can speak on a subject as long as he likes. As long as they do not break for water/bathroom/etc or in anyway yield control of the floor, a senator may speak as long as they like. Strom Thurmond famously filibustered the Civil Rights Act for over 24 hours.

In modern times, the Senate doesn't actually require a senator to take the floor and speak to filibuster. All he must do is tell the party's floor leader, I believe.