Why is the centripetal force necessary for circular motion?

The centripetal force can be thought of as the force that causes circular motion.

When an object moves in a circle a force must always act on it, even when it moves at a constant speed. This is because velocity is a vector (and therefore has both a magnitude and a direction) and the direction the object is moving in is constantly changing.

This constant direction change is an acceleration, and we know from Newton's Second Law that any acceleration must have an force associated with it.

Similarly, the centripetal force must point towards the centre of the circle, and therefore perpendicular to the tangential velocity, to maintain the motion in the circle. If it did not exist the object would 'shoot off' in a direction tangential to the circle.