Implies dishonesty and is used negatively to describe someone's character. I wouldn't trust Nancy with the cash register; she's got sticky fingers.
Pro Tip 2/3
Metaphorical Usage
It's not about literally having sticky hands but about someone's tendency to steal. Ever since the jewelry went missing, everyone says he has sticky fingers.
Pro Tip 3/3
Colloquial Expression
Used in informal situations, often in casual conversation, not formal writing. Our new roommate has sticky fingers; my snacks keep disappearing.