This idiom or expression has to do with:

Doing something wrong and not getting caught or, if caught, not getting punished for it.

Q. Did they catch the guy who stole your car?
A. No, he got away with it.
Q. But they caught the guy who stole your bike, right?
A. Yes, but he got away with it, too. I guess he was good at explaining things!

Related:
Getting away with murder!

Also see:
Beating a rap.