I am neither a scientist or physicist, but fascinated by it all.

Think of time as a grid drawn on your bed mattress. Under normal circumstances, the lines are all straight and even. If you put a marble on the bed, it would not change the gridlines significantly - the "time-grid" would not be distorted much at all. if you put a heavy bowling ball on the mattresss, the grid would be deformed as it goes around the ball.
An object that may be travelling across one of the un-distorted grid lines, travelling at a constant velocity, would move from one one side of the bed to the other at a certain measure of time. If you sent a second, similar object travelling across one of the distorted gridlines below or around the bowling ball, it would experience an area where the "time-space-grid" is deformed. Since its velocity does not change, but it has "farther" to travel as it follows the grid around the ball, it would arrive at the other side of the bed at a time later than the first if you compared the two relative to each other. If both objects were traveling at the speed of light and had pilots inside, the two objects would arrive at the other side of the bed at different times, relative to each other. The confusing part comes that when the watches of the watches of each Pilot are viewed, both would show the exact same time as they cross the finish line.
Now if the object you placed on the mattress was heavy enough to deform the top of the mattress (and the grid) to the point that you could not even see or reach the object, but it stretched the grid indefinitely, then the object travelling across the grid at this point would seem to disappear as it headed towards the deformity. If it was truly a black hole, the travelling object would never come out.
Consider a light photon travelling instead of the travelling object, and you can see the reason that light never exits a black hole and time is distorted indefinitely.

If this helps explain the concept better, tip ArchSteve
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