Non-contact forces are the forces which can come into play even when objects do not have any physical contact between them.
Opposite poles of two magnets stick together because of the attraction between them. This attraction can be felt even at some distance when the magnets have not stuck to each other.
Which means that magnetic force do not necessarily require direct contact between the objects to come into play. Therefore, it can be concluded that magnetic force is a kind of a non-contact force.
Likewise, objects lying on the surface of the earth can experience the force of gravity which is a non-contact force.