What is potential energy?

When most students start their physics courses the first form of energy they learn about is kinetic energy which is related to the velocity that an object has. Conversely, potential energy is a form of energy that is related to the distance or position of an object with respect to other objects. It can be thought as the potential or capability of doing work. Whenever an object has potential energy it is due to some other object changing its position and the storing of energy as a result of this change of position.
For example, if I have a spring that is slack initially, and I then compress the spring, what happens? The spring gets firm and stiff and if I release it, it then shoots forward at high speed. In this case the spring initially has no potential energy since it can't move or do work on any other object. However, if I then compress the spring then I am changing the starting position of the spring. The spring gets stiff and energy is stored as a result, prescisely how much energy is stored depends on how much I change the original position of the spring. The more I change the position the tighter then spring gets and the more energy gets released when I let go of the spring.
For this reason potential energy is often thought of as the work done on an object since you must always to work on an object to change its position.