It seems like you know about filibusters, but not about Cloture. A filibuster can be ended if a 60% supermajority of the senate votes for Cloture. Basically, what the filibuster does is prevent the passage of any bill that 41-49% of the senate really, really does not want passed.

People like it because it makes the distinction between having a majority (51% of the Senate) and a mandate (60% of the Senate).