It means that you're in a better situation.
For example, "There is a storm coming so you're better off if you stay inside today."
It means that since there is a storm coming, it will be better for you to stay inside.
It suggests that your situation will be better compared to some alternative.
It's commonly used when two people end a relationship/friendship. "She'he never really appreciated you, so you're better off without him/her."