Einstein has come up with two theories of relativity: "special relativity", and "general relativity".
Special relativity is the study of how measurable quantities such as: intervals of length, intervals of time, and inertial mass depend on the relative velocity of an object. His conclusions were based upon the (at the time) revolutionary assumption that the speed that we measure light traveling at does not depend upon the velocity an observer is traveling at. (note: it was THIS theory that he came up with when he was a patent clerk).
The findings are that an observer traveling on a rocket ship at a constant (but very high) relative velocity will look out and see that time outside the rocket's window moves slower than time does inside the rocket ship; that length intervals measured along the direction the rocket is traveling will shrink; and finally, the inertial mass of passing objects will also increase dramatically.
The ideas that the rate that time passes, and that there is no such thing as a fixed length is revolutionary and quite counterintuitive. Indeed, understanding the world of special relativity requires a whole new physical intuition. It is all, however, a simple consequence of having a constant speed of light. The constancy of the speed of light has been tested time-and-time-again, and it is a verifiable fact.
General relativity, einstein's second relativity theory, is a lot more difficult. While special relativity can be taught to a high school student, General relativity usually requires several years of physics instruction before it can be properly understood.
It is, as the name suggests, a more General Theory. The idea, in short, is that there is something called "space-time", and that matter causes space-time to bend. The effect of the bending of space-time is what we call "gravity".
Ever notice how all object, regardless of their mass, fall towards earth with the same acceleration? Einstein did too! This realization is one of the fundamental basis of General relativity.
Since it is space-TIME that is bent by massive objects, one result which general relativity predicts is that time will pass SLOWER the higher the gravity is. SO, time passes slower on earth than it does on the moon, or in orbit around the earth! this difference in the passage of time is very slight, but it has been measures.
incidentally, if you fall into a black hole, the curvature of space-time is so violent that the universe outside the black hole will experience an INFINITE amount of time as you cross the "event horizon". So there's NO GETTING OUT, because there's nowhere to get out to! hahahaha