Constructors are the different teams in the game, There are 14 different constructors each with two drivers.
All you need to do is complete any event with all 14 constructors, winning is not required but you do need to place in the top 3. Belgium is the shortest track in the game if you wish to rush though this.
The constructors are:
You can see which constructors you have/have not played an event with in 'My Stuff - Statistics & Collection'