Your Wanted level represents the level of crime you have commited at a specific time. It is represented by one through six stars. At each different level a new kind of authority will pursue you or they will do so differently.
With a wanted level of one star, it is common for cops to bust you by opening the door of your vehicle if you are going slow. They will come after you if you are near them, but they will not go out of their way to get you or call for backup. They will shoot you if they cannot reach you or hit you hand to hand.
When two wanted stars are attained cop cars will come after you and more police officers will appear on foot than usual. At this level and higher they will try to "waste" you more than bust you. They do this by shooting at you and by ramming into your vehicle.
At three stars, another Miami Vice reference is introduced. At this point, two law enforcement officers will show up in a Cheetah who closely resemble Don Johnson and Phillip Michael Thomas, who played the main characters in Miami Vice. Interestingly, Philip Michael Thomas also voices Lance Vance.
Anyway, these officers have machine guns which will kill you much faster; also, the Cheetah is much faster than the Police Car for road chases. Also at this point the police will form road blocks with their cars.