GRAVITY WELL

In physics, and specifically with respect to the theory of general relativity, a 'gravity well' is a distortion in space-time caused by a massive body such as a planet or star, or any other object which has mass. The term is a reference to the 3-dimensional analogy of this phenomenon: an extrusion of an otherwise 2-dimensional sheet. An actual gravity well involves higher-dimensional bending. A black hole is an extreme example of a gravity well which is stretched infinitely and time slows down to the point where it is not noticeably moving.
The "depth" of a gravity well corresponds to the Δv required to leave -- also known as the escape velocity. Deeper wells require more Δv, and so it is harder for a rocket to escape from them (or to stop at the bottom). Deeper wells also tend to make for more efficient gravitational slingshots.
Because both space and time are altered in a gravity well, not only are objects attracted towards it, but time slows in its presence due to the effect of general relativity. This effect is more pronounced as the gravity well gets larger or as one proceeds closer to its center. Think of a gravity well as a sheet of stretched rubber, a small object, such as a planet or moon, will make a small dent in space-time. A larger object, such as a star, will make a larger dent in space-time and a black hole makes a very large dent, so large in fact that it has an escape velocity higher than that of the speed of light. The "dent" in spacetime is so large, that it closes the "sheet of rubber" on itself, creating an event horizon where the events inside the horizon are not observable by any known methods.