NPR says the term filibuster “first appeared in the English language in 1591, according to the Oxford English Dictionary. The word was then `flee-booters’ [for ‘pirates’]. Its origins are probably Dutch, with some Spanish and French influences.” The pronunciation changed over time to our modern “filibuster”. In 1890 an obstructionist legislator was called a filibuster, and the word was on the road to our modern usage.

Online Etymology agrees with the origin of the word.

Free Republic offers more detail on the rise of our current usage.  In the early 1800s Senators began making long, irrelevant speeches on the Senate floor, which delayed or even stopped votes on legislation.  Battles over how to deal with the tactic ended in favor of the obstructionists, who were called filibusters by their opponents.  Today the old meaning is lost.  To filibuster is to disrupt and interfere with legislation through delay on the Senate floor.