Leagues what are they?

Not sure I understand wha the advantage is to climb the league division.
Anybody care to shed some light on the advantage on been in a division?

It's similar to other online game leagues. It's a way to measure how active in live play someone is really, as it stands today. Or how active they've been in the past if they're stuck on a League (like me )

Understood, but is there any benefits?
Say I climb the ladder and I get to the top, what do I get for it? Better matches? Less likely to play a cheater? 
Usually there is some benefits in been in a better league, but I don't see any of them here.

No. Legend league used to have prize tourneys but the site has that on hold and it deciding what to do with that level but other than that, nothing special at this point (other than achievements)