Missions are a method to essentially help level up and earn Cash fast. You go through missions first during the tutorial, which guides you to the types of missions. On some occasions, you end up getting wanted as part of the mission and you must lose your Wanted Level or get back to a certain area (timed or not).
There are six types of missions in the game:
Kill & Beat-up missions
Indicated with a skull, these missions require you to kill people with a certain weapon or beat them up until they fall. Occasionally it requires you to run over a target with a vehicle.
Racing, Car Wrecking and Chump Killing Missions
This mission is indicated with a racing car with a purple background. The missions assigned to the player are racing (in a car), racing (in a helicopter), blowing up cars and killing chumps. These missions are usually timed, except the racing (car) ones.