It is like shop lifting but you steal things from a bar instead of a shop. You usually steal things like an ash tray or a cool shot glass. It is usually unnoticed and if noticed you usually don't get punished.
On the phone...
Amber: Hey Dick. How's it goin'?
Dick: I'm cool Am. I barlifted this cool martini glass. You wanna trade with you lucky strike ash tray?
Amber: Barlifting is cool.