The purpose of a filibuster is to prevent a piece of legislation from being passed in the Senate. A Senator seeks permission to address the Senate and continues talking for an indefinite period of time in an effort to delay or discourage a bill's passing.
The Senator delivering the filibuster speaks on anything he wishes, even reading from a book or historical documents if he wants to do so. As of the beginning of 2014, the longest filibuster in history lasted for 24 hours and 18 minutes. Senator Strom Thurmond, filibustering against the Civil Rights Act of 1957, holds that record. The bill eventually passed. Filibusters only take place in the Senate because of laws in the House of Representatives that prohibit them.