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An area, echelon, or sphere of great competition, success, power, achievement, etc. Refers to major (i.e., "big") leagues of sports teams. I know you're new here, but you need to perform much better than that. You're in the big leagues now. Welcome to the big leagues, senator.
An area of tough competition and high rewards; the largest or foremost of its kind. For example, Winning an Oscar put this unknown actress in the big league. The term alludes to the major (big) leagues of American baseball. [Late 1800s] Also see big time, def. 2.
1. n. a situation where competition is keen and a high level of performance is expected. (Usually plural. Referred originally to major league sports.) You’re in the big leagues now—no more penny-ante stuff.
2. and big-league mod. professional; big time. (From baseball.) When I’m a big-league star, I’ll send you free tickets.