What is the "Nuclear Option"?

People for the American Way explains:

As the name suggests, the "nuclear option" is a radical tactic that would prohibit senators from using filibusters against extremist judicial nominees. Right-wing senators and leaders are supporting this destructive action because they want to guarantee the Senate confirmation of far-right ideologues to our federal courts, especially the Supreme Court. The "nuclear option" is actually a series of steps that right-wing senators would take to eliminate the filibuster. The "nuclear" attack would likely begin with one party’s senators provoking a filibuster, most likely by trying to force a confirmation vote on an out-of-the-mainstream appeals court nominee. A senator would then object, claiming that the filibuster cannot be used on a judicial nomination. Vice President Cheney or another senator presiding over the Senate would rule in the Radical Right's favor, and then that ruling would be appealed. A simple majority (with Vice President Cheney as the tie-breaking vote if necessary) would then uphold the ruling, and the filibuster would be history. The "nuclear option" earns its alarming name for two reasons. First, it breaks the Senate rules in order to eliminate another rule: the filibuster. Under normal Senate procedures, it takes 67 senators, or two-thirds, to end debate on changing a Senate rule. The "nuclear option" would violate Senate rules and require only 50 senators plus the Vice President's tie-breaker. Second, the atmosphere in the Senate after this attack would resemble a "nuclear winter." All bipartisan cooperation would vanish and the Senate's legislative business could grind to a halt, only adding to the price Americans would pay for the right's reckless abuse of power.