Actually, the answer to this is not so complicated. The reason it appears to be a unique feature of Black Holes is that the effects are very pronounced in that case, but changing of time is an everyday event, throughout the universe (i.e. even in your own back yard...).

Suppose you toss a ball into the air and inside the ball is another ball. If the outer ball was being acted on by a force, it would move -- pushing against the inner ball. Yet, somehow, when gravity pulls on the outer ball, is also pulls on the inner ball with just enough force that the two balls accelerate together. This is a fairly unlikely scenario given you don't know the composition of the balls or that you could change the mass (and hence the force) easily for one of them.

Einstein didn't like this notion either -- and came up with an idea: he claimed that the force of gravity is nothing more than an acceleration, so that the force you feel in an elevator is really just gravity, not gravity plus some other force. In this picture, a falling elevator (in which the objects inside feel no force) is indeed not under the influence of a force, despite the fact it is accelerating relative to the building it is in. On the other hand, he would argue that a 'motionless' elevator does sense a force, as every object in it is mashed to one side by the acceleration. This broadly described the principle of equivalence between an accelerating frame and a frame under the influence of 'gravitational force'.

How can a body which is not moving be accelerating? Remember that acceleration is defined as change in velocity with time or change of change of position with time. Here if position is constant, it would appear that acceleration is zero. However, what if TIME was passing at a different rate (slower) closer to a large massive body (like the earth). In that case you would still have acceleration, without motion, and if you had no acceleration, you'd have to be moving (falling). This is precisely what is meant by time moving slower -- time really is moving slower closer to the surface of the earth than in orbit and gravity is the consequence of this behavior. The reason that you don't notice time moving slower, is that there is a pretty large constant setting the time scale from the distance scale -- the speed of light (~300,000 km/s). Because of this, over distance scales of a inches or miles, the shift in time is very, very small, but is still significant as you have seen. (objects which are not accelerated tend to quickly move this close to the earth).

>Close to a black hole, the acceleration gradient is very much higher -- so much so that the difference in time delays becomes infinite as you approach the surface. If the hole was large enough, you could even survive the gradient (tides) due to the difference in time speed between your head and feet. If the earth was packed into a black hole, all its mass would be packed into a ball about a cm in diameter -- you can try to imagine the tides from such a source.

As it happens, by many experiments, (even flying atomic clocks in orbit), these effects have been observed and validated, so this theory is working practice. Always, remember, however, it is only one step closer to the truth, and will be revised when better models and theories are validated.