Filibuster, also known as talking out a bill, is  a tactic of parliamentary procedure.

History
The term "filibuster" comes from the French word "flibustier," meaning "pillaging pirate."  In terms of parliamentary procedure, the word was not used until the 19th century However, the use of long speeches as a delaying tactic is part of the history of the Roman Senate. For example, Cato the Younger is known for using filibuster tactics to block Julius Caesar's rise to power.

Timeline
1841: The first ongoing filibuster in the United States Senate starts on February 18 and ends on March 11
 1853: The term "filibuster" is first recorded in the Congressional Record
 1874: Joseph Gillis Biggar delay the passage of Irish coercion acts by making long speeches in the British House of Commons to  
 1880:  The long speeches of Charles Stewart Parnell in the UK House of Commons blocked debate on anything else; and the tactic forced Parliament to take the issue of Irish self-government
 1917: The US Senate adopts the cloture rule in order to limit filibusters
 1919: A filibuster in the US Senate held up a vote on the Treaty of Versailles
 1957: US Senator Strom Thurmond holds record for the longest filibuster. His 24-hour, 18-minute speech on August 28-29 was against a civil rights bill.
 1964: The Civil Rights Act of 1964 is approved after surviving an 83-day filibuster in the US Senate
 1983: British Member of Parliament John Golding talked for over 11 hours to delay the British Telecommunications Bill
 2011: A filibuster about Canada Post by the New Democratic Party (NDP) in the House of Commons of Canada started on June 23 and ended on June 25, 2011.
 2013: Chuck Hagel, the president's defense secretary nominee was filibustered after a cloture motion (the vote that ends the filibuster) failed 58-40.

United States 
In the United States, a filibuster allows a senator to block a bill he or she does not like by speaking on behalf the bill for too long on purpose so it would not be brought to a vote. 

Current rules in the Senate must allow any Senator to debate for as long as they want. Since they're not limited to how long they're allowed to speak, they can refuse to end debate. To break a filibuster requires 60 out of 100 votes known as a "cloture". If the cloture is successful, debate ends whereas an unsuccessful outcome allows debates to continue. Bills cannot be voted on until all Senators are finished giving their speech or a cloture is agreed to in which senators can no longer debate on a bill.      

Only reconciliation bills are immune from filibusters and can be passed by a simple majority. In 2013, the filibuster rules were changed to prohibit filibusters for voting on the president's nominees for agencies and courts with the exception to appointing judges to the Supreme Court of the United States. In 2017, Senator Mitch McConnell changed the 2013 rule to add the "nuclear option" to block Democrats from filibustering Neil Gorsuch's confirmation to the Supreme Court as appointed by then-President Donald Trump.      

In 2021, the Democratic Party introduced legislation that would eliminate the filibuster that could be passed with only a majority vote. However, Democratic senators Joe Manchin and Kyrsten Sinema said they are opposed to ending or modifying the filibuster.

References

Other websites
 "Filibuster and Cloture" at United States Senate

Politics