For an object moving in a circular path, the centripetal force is any force which acts towards the centre of this circular path. This means it acts perpendicular to the direction of forward motion.
It is important to remember it is not an additional physical force like gravity or friction. It is simply a TYPE of force, which may be provided by gravity or friction. For example, for a planet orbiting the Sun, the centripetal force is provided by gravity, as gravity is the force acting towards the centre of the orbit.
The formula for centripetal force is:
F= mv2/r = momega^2*r
where m is the object mass, v is the linear velocity, omega is the angular velocity and r is the radius of the motion.