The "major leagues" are the highest level of professional sports, especially baseball in North America. Figuratively, it means the top tier or big time in any field, with high stakes and elite competition.
I'd like to help educate kids about the Major Leagues - what to anticipate, what to expect, what they'll need to do to prepare themselves. Barry Bonds
I perform in the major leagues of what I do. It's incredible. Darrell Hammond
All of a sudden I'm in the major leagues and we're traveling from town to town. I see the other players dressing different every day. I've got only one suit and I keep wearing it over and over. I'm really embarrassed. Al Kaline
Well, I wanted to play twenty years in the major leagues. I never made it twenty though. I played nineteen. Bert Campaneris
Not many people get to the major leagues and succeed right away. There are some struggles. Everyone seems to struggle. George Brett
But baseball bounced back in the next decade to reclaim its place as the national pastime: new heroes, spirited competition, and booming prosperity gave birth to dreams of expansion, both within the major leagues and around the world. John Thorn