why do they call the ncaa tournament the dance?

Answer 1

Colleges have their prom and homecoming dances and it was an indication of your popularity and or importance to be invited to those dances. I think that when the NCAA selection committee invited teams to play in the NCAA tournament the phrase "invited to the big dance" was coined to be a clever way to describe the process much like an invitation to a college dance.

Answer 2

I believe it's called the "big dance" because it is an expression meaning something that is very, or most, important.