A filibuster is simply a procedural rule that allows a Senator to continuously talks for, well as long as they can talk uninterrupted. Mind you there are some rules that allow this person to take a rest here and there another Senator, presumably someone sympathetic to their cause, can ask a question. This isn't a simple as "hey can you clarify that last remark", these questions are intended to give the person filibustering an opportunity to stop talking. So you may see a Senator ask a question that could be in 37 parts and could take anywhere from 10-15 minutes to actually ask the question in hand.
According to the Supreme Court ruling in United States v. Ballin (1892), changes to Senate rules could be achieved by a simple majority. Nevertheless, under current Senate rules, a rule change itself could be filibustered, with the votes of two-thirds of those senators present and voting (as opposed to the normal three-fifths of those sworn) needed to end debate.
Cloture is the process of ending debate... In order to achieve cloture under the current Senate rules you need 60 Senators to vote for cloture. In other words you need 60% of all Senators to agree. So why is cloture so important. Take a look at this chart.
This chart shows an explosion of filibusters starting in 2005. Mostly led by the Republican Party and their effort to block any legislation from being voted on in the US Senate. Harry Reid, the Senate majority leader, uses cloture as a means of moving debate a long and getting something, anything done in the US Senate. The filibuster which was originally designed as a check on raw power of the majority in the the last 10 years has been used as a tool to stop the business of government as a whole.