With 60 votes, the senate can end/forbid filibusters, a traditional means of interfering with or ruining unwanted legislation that the smaller party could not otherwise block. It's an odd tactic, with various rules determining how it can be employed, but the simple explanation is that a senator can take the floor and begin talking, preventing the Senate from continuing with business until he stops, they get 60 votes to stop him, or the bill is withdrawn (his goal).