Let us first look briefly at how a bill becomes a law so that we will have some idea of how the filibuster and cloture enter into the process.
In a nutshell, a bill must pass both houses of Congress in order to go to the President to be signed into law. The two houses of Congress are the Senate and the House of Representatives. Both must pass identical bills in order for that bill to be sent to the President. The filibuster and cloture exist only in the Senate.
In order for the bill to pass the Senate it must, of course, be voted on. However, by the Senate rules, there must be at least 60 Senators who agree in order for a bill to get a vote. This is where a filibuster comes in. In the modern form of this procedure, Senators who are very opposed to the bill refuse to allow it to be voted on. This is called a filibuster. In the old days, they had to get up and talk non-stop to prevent a vote from happening. This no longer happens today except in very rare circumstances.
If a group of Senators filibusters a bill, the supporters of the bill may attempt to invoke cloture. Cloture is when 60 or more Senators vote to end the filibuster and force a vote.
Thus, a filibuster is a way for a minority of Senators to obstruct legislation they do not like and cloture is a way to overcome their filibuster.