Centripetal Force is the tendency of a body to follow a curved path towards the center of curvature. Isaac Newton described it:
A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center. [Wikipedia]
Simply put, an object affected by a "pull" action -- whether a binding force like a rope or by gravity -- will follow a curved path while in constant motion. If the action of motion ceases, the object might remain in place, or it might fall towards the binding force, depending on how it is attached or not attached. Centripetal force is often confused with Centrifugal Force, which is the force exerted by the orbiting object on the center.
In an amusement park, the most common usage of centripetal force is on Roller Coasters, where the car is partly fixed to the track by its own speed and weight. The tendency of an object to travel in a curved path pushes the car against the track harder when it goes around a curve or upside-down in a loop, thus making the action of the car safer. If the car were to stop at the top of a loop, the centripetal force would cease, and the car would react to the Earth's gravity as any other object; it is the speed of the car which generates the centripetal force. The faster the car goes, the more it is "pushed" against the track; this is not necessarily a matter of safety, as a car going too fast might jump the tracks as the speed exceeds the ability of the car to make turns.