What is cloture?
The Senate procedure that turns a majority into 60 votes.
Cloture is a motion to end debate. It is the Senate's only mechanism for cutting off discussion when a senator does not want to stop talking.
The threshold
Invoking cloture on legislation requires three-fifths of senators sworn — 60 votes when all 100 seats are filled. That number does not change with the size of the majority.
Why 60 became the working majority
Because any senator can withhold consent to end debate, the practical requirement for passing most legislation is 60 votes, not 51. A bill with 55 supporters fails, and the recorded vote you see may be the cloture vote rather than a vote on the bill itself. This is why a roll call can show 55–45 next to the word "Failed".
The exceptions
Nominations require a simple majority (changed in 2013 and 2017). Budget reconciliation bills are limited to 20 hours of debate and cannot be filibustered, which is why so much major legislation is routed through reconciliation.
Reading it on this site
When a vote page shows a question containing "Motion to Invoke Cloture", the tally is about whether debate ends — not about whether the underlying bill is approved.