The Mob Wars part of the game takes place on a map of New York, divided into conquerable territories. As each turn begins, you'll draw a hand of cards that enable you to do things like bribe the police for protection, forge a truce with a rival or call in a hit on his turf to weaken its defense. You can then hire mobsters to defend your territories, play your cards and move your goons into unoccupied or rival turf.
If it's unoccupied, you'll get to engage in a little extortion by talking to a shopkeeper and convincing him to pay protection - usually by slapping him around a little or smashing up his shop. After he caves, you'll be able to stomp into the back-room racket and buy it out. Then you can mark off another territory that's paying tribute to the Corleones.
If the space is occupied, things get a little more complicated, and you'll be tasked with pulling a hit or bombing a business, both of which require fighting through squads of mob goons. And if it's a family compound, you can take your rival out of the game by planting bombs in two different houses - just be aware that they're swarming with goons carrying tommyguns.
It's kind of a letdown that the Mob Wars portion is single-player only. It's also strange, considering signs that it was originally supposed to be multiplayer - like a card that enables you to make a truce with the Corleones, the only family you can work for - were left littered throughout the game. Even so, it works well enough as a quick, moderately strategic alternative to the story mode.