1. noun
a) An association of sports teams which plays at the highest skill level of its sport, especially Major League Baseball.
You cant be so casual. Youre in the major leagues now.
b) The highest level of competition in a field of endeavor.
2. adjective
a) Of or pertaining to a major sports league.
That rock band is really major league.
b) Analogous in importance to a major league sports team.
Calatrava is a major league architect.
Wikipedia foundation.