definition - something or some group that is outstanding of its kind (as in stature, quality, or worth)
Big league has a fairly literal meaning (“major league” or “any comparable sports association”) which has been in use since the 1870s. The figurative use defined above is often found used in an attributive sense, in which it modifies another noun (“a big league politician”). Big league is sometimes phonetically confused with bigly, an adverb that means “in a big manner.”
It has been let out, that the Evansville club was not organized for the purpose of going on a round of victorious games, but only to play against the big league clubs, to let our citizens have a sight at the way professional muscle can handle the ball and bat.
— Evansville Courier and Press (Evansville, IN), 17 Jun. 1877