The setup for the pilot is that there are four brothers, three of which are hoodlums involved in pseudo-organized crime (small scale stuff, they help 'run' the neighborhood). One of the brothers is a good guy, has a promising life as an artist that everyone is proud of and wants nothing to do with his brother's life of crime.
But when one of his brothers is sent to the hospital in near death due to a dispute with a rival crime family, he decides to sacrifice his future to save his family and kills the rival crime boss, and inherits the neighborhood as a result. They pretty much took Michael Corleone and made him Irish.
What's even worse is that it's not even the best Irish crime/mob drama on television, because Brotherhood did it on Showtime and better.