The word itself isn’t in the Senate rule book and only started to pop up in the 1850’s, but it does have a commonly accepted definition in modern-day Senate procedure.
A filibuster, as the Senate Historical Office considers it, is an effort to delay or block legislative action by preventing a vote.
There are a few types of filibusters, including the “talking filibuster” of “Mr. Smith Goes to Washington” fame, in which a senator takes the floor for hours (and hours) on end, going so far as to read the phone book or other lengthy literature to kill time, until the Senate leadership gives up and pulls the bill in question from the floor.
Those dramatic proceedings have been replaced with a much more common – almost routine – effort to block legislation, in which one senator objects to an up-or-down vote on a measure or confirmation, frequently signaling such intention behind the scenes. That, in modern practice, is what a “filibuster” usually entails and is what most senators refer to when they mention the maneuver.
In this case, rather than proceed straight to the vote – for example, the Gorsuch confirmation, which only requires a simple majority – the Senate must first debate the measure, for up to two days, and then vote to end debate, which is known as a cloture vote.
This is what Senate Democrats are doing in the Gorsuch case. They have filibustered the confirmation vote, and under the current rules, Republicans do not have enough votes to break the filibuster, or pass the cloture vote, which requires 60 votes to confirm.