When a body or a collection of particles is acted on by external forces, the center of mass moves as though all the mass were concentrated at that point and it were acted on by a net force equal to the sum of the external forces on the system.
This result is central to the whole subject of mechanics. In fact, we’ve been using this result all along; without it, we would not be able to represent an extended body as a point particle when we apply Newton’s laws. It explains why only external forces can affect the motion of an extended body. If you pull upward on your belt, your belt exerts an equal downward force on your hands; these are internal forces that cancel and have no effect on the overall motion of your body.