The filibuster and cloture
The Senate, unlike the House, normally lets debate run without limit. Ending debate over objection takes 60 votes, which is why so much legislation needs a supermajority to pass the Senate at all.
Unlimited debate
The Senate has no general rule forcing a vote. A senator, or a group of them, can hold the floor or simply decline to consent to ending debate, a tactic known as the filibuster. Without a way to cut it off, a determined minority could block a measure indefinitely.
Cloture: the 60-vote off-switch
Cloture is the only formal procedure for ending a filibuster. Under Senate Rule XXII, invoking cloture on most legislation takes three-fifths of all senators, 60 of 100, and even then allows up to 30 more hours of debate before the final vote. Because 60 votes are hard to assemble, the practical threshold for passing contested legislation in the Senate is 60, not a bare majority of 51.
Why the House is different
The House has no filibuster. Its Rules Committee places time limits on every major bill, so a simple majority can move legislation through. This is the single biggest procedural difference between the two chambers.
Nominations are now a majority vote
The Senate changed its own precedents, in 2013 for most nominations and in 2017 for Supreme Court nominees, so that cloture on nominations now requires only a simple majority. The 60-vote threshold still applies to ordinary legislation.