The Pickpocket page is where you go to steal from other players.
In order to pickpocket someone, they have to be online and within three tiers of your current rank. (i.e. A Wise Guy can pickpocket up to a Boss [(1) Made Man (2) Capo (3) Boss]).
If someone picks your pocket and you catch them (it isn't stealth), you have the ability to "Mug" them back. This is much more severe than a Pickpocket, and hasn't a limit on how much money you can take (however, you can only take money they have on-hand, not in banks). There is also a small chance that during a mugging you can lose possession of your gun. If the mugger has no gun and you trigger the small % that will cause you to lose possession of yours, he may take it. Mugs also affect flight, wack, and pickpocket timers, extending them by a random amount.