Centripetal force is a force that is acting on an object if it is orbiting around another object. This can happen to a planet as it orbits the Sun or it can happen to a weight that you tie to a string and swing around your head.
In both cases, there is a force that pulls that object back towards the center -- towards the thing around which the object is rotating. So centripetal force is the opposite of centrifugal force. Centrifugal force pulls the orbiting object away from the center while centripetal force pulls it towards the center.
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Centripetal force that is constantly acting on a object that is moving in a circle at a uniform speed. This force is always acting toward the center of the circular path. When such an object continues to move in its circular path without being pulled towards its center, the centripetal force must be balanced by an equal and opposite centrifugal force.
A common example of this kind of circular motion is provided by moon orbiting the earth. The moon continuously orbits the earth under the influence of centripetal force acting on the moon due to gravitational pull between earth and moon. The reactive centrifugal force is provided by the momentum of the moon as its velocity changes to maintain circular path. This way, the moon continues to orbit earth without either being pulled to the center of the earth or being forced away by its momentum.
For a body to move at the same velocity, in a linear direction or a circular direction, the net force acting on it must be zero. Now for a body that is rotating, there is a force acting away from the point around which it is rotating. This is evident from the fact that if you try to rotate a mass tied around a string and let go of the string, the mass flies outwards. This is due to a force called centrifugal force.
To counter the centrifugal force another force called centripetal force is required. This is pointed towards the center of rotation. It is the result of differing causes, for example the gravitational force between the Earth and the Sun provides the centripetal force in this case. For electrons rotating around the nucleus of an atom, it is electro-magnetic attraction between the protons and the electrons.