What does 'She gives as good as she gets.' mean?

Depends on context, but the usual idea is that the person is able to defend herself.  She can give out as much as anyone can attack her with.  Usually not meant in physical terms, but rather in terms of verbal conflict, but can mean actual physical confrontation.  She isn't a pushover, but instead can hold her own, even maybe win, if she gives as good as she gets.

When she is involved, the fight will be fair because she can give as good as anyone can try to give her.  She can respond equally.  The match is equal.

It means she doesn't allow herself to be a victim.

This means that this person is not allowing anyone to bully her. If someone picks on her she fights back.

you do back to people whatever (mean) thing they're doing to you.

Don't get it? Now put that context in bed. Get it now?