Just to add my two penn'orth (as we say in Britain):
'Cheers' has three main uses:
1. As a toast.
When in company, you raise your glasses before drinking and say 'Cheers!'
Usage = Throughout English-speaking world.
2. To mean 'Thank you'.
This is an informal, casual expression of thanks, for a minor favour or service, as Dewey and Richard have explained.
Usage = British - but not universal. It's used more by males than females, and more by younger people than older ones. 'Cheers, mate' would be a typical informal way that one British man would thank another one. I've never said it in my life.
3. As a sign-off for a note or email - a more informal version of 'Best wishes', as Christopher describes above.
Usage = I'm not sure, but this seems to be mainly American.