A Contact force as the name suggests acts on a point of an object by direct contact. The Contact may be Continuous or sometimes momentary. The former case is known as Continuous force and the latter case is known as impulse force.
example:
1) Pushing an object along the floor :
This is an example of a continuous force. Here, continuosly, the direct force is put on the object to move it along the floor.
2) Kicking a Soccer ball :
This is the example of a impulse force. Here force is applied to the ball with a given mass for a given time and we can see the ball is moving away with some velocity in a particular direction.