Centripetal force is just the name we give to a force acting towards the center of some circular motion. The particular forces that give rise to the centripetal force depend on the particular circumstances. In the case of a satellite in orbit around a planet, gravity provides the centripetal force.
Since the satellite is centripetally accelerating, there must be a net centripetal force (provided by gravity). Since that force remains perpendicular to the motion, the satellite continually changes direction. Note that forces cause changes
in velocity. Since the force acts towards the planet, the change
in the satellite's velocity is towards the planet. (If the satellite were not moving, then it would surely fall. But it is moving--at just the right speed to maintain a circular orbit.)