These past few days the word filibuster has shown up everywhere and I'm trying to understand how it relates to McConnell and how it affects the Democratic Senate majority.

From my understanding, a filibuster is used to delay a vote in the Senate. According to NY Times: "By exploiting the chamber’s rules for full debate on an issue, the minority can indefinitely obstruct something that has majority support." In other words, if someone keeps on "debating" then the Senate won't be able to hold a vote where a simple majority (51 of 100) passes the bill. Apparently it's been used extensively by Republicans to defeat a ton of bills.

Then yesterday I read in NY Times that McConnell Relents in First Filibuster Skirmish, but the War Rages On. Essentially it says that McConnell dropped his demand for the Democratic Senate majority to promise not to eliminate the filibuster. What would've happened otherwise?

Then I found this NY Times article that explains the filibuster and its use with an SC: The Senate Filibuster, Explained. It didn't help much, especially when it talks about "cloture", the 60 votes needed to invoke cloture, and the nuclear option:

How does it work? The Senate generally operates by unanimous consent. If any senators refuse to consent to holding an up-or-down vote on Judge Gorsuch’s nomination, the Senate has to decide whether to overrule them. It would do so by holding a “cloture” vote on whether to end debate and proceed to a final vote. It takes 60 votes to invoke cloture, so 41 senators can indefinitely block a confirmation by refusing to vote for cloture.

Obviously a filibuster isn't as simple as saying that it's a way to delay a Senate vote. And if it can be eliminated, then why didn't McConnell eliminate it when he was Senate majority leader?

Not only that, I've seen it used as a verb (filibusted) and there are different variations (In 2013 the Democratic Senate "used the nuclear option to eliminate some other types of filibusters")