Essentially fully comp means you are covering your own car for damage in case of a bump that's your fault.
If you have a 3rd party policy it means you would not be covered for damage to your car. Some people take that cover, because it is cheaper(not a lot mind) than fully comp because of the value of their car. For instance if I drive a car that is probably worth £500, by the time the excess off it would not be worth claiming/repairing the car.