A gravity well
is the name for the depression in space-time
that any large body produces.
According to General Relativity, gravity doesn't only make things fall down, it also literally bends and stretches space.
For example, the space inside the earth 'sags'. Imagine if you had laid a rubber disk on a lighter rubbery membrane- the disk will sag in the middle; and so if you measure the diameter of the disk, from the outside with callipers, and then compared it by measuring the diameter of the disk by running a wheel across the disk, you will find that the internal diameter of the rubbery disk is bigger than its external.
The earth does the same thing, but in three dimensions. For instance if you could actually drill a hole through the earth the distance through the earth is actually more than it's external diameter. However the difference in distance is going to be very tiny.
This distortion of space-time extends not only within the earth but outside it too; although it weakens as you get further away.
Indeed, that's how we know for sure that it is a real effect. The external distortion of the sun has been detected by noticing how starlight bends past it; so this isn't only a theoretical effect.
Hence the Earth sits in the middle of a little well of curved space. Hence gravity well.