Imagine you’re a flat person, 2 dimensional, and you live on the surface of a balloon. Your movement is restricted to the ballon surface – you live in a curved 2D space. Now, imagine the balloon is being blown up at a constant rate. You can think of time as being the radial dimension, the 3rd dimension. Being a 2D person, you can’t move in the 3rd dimension but you experience it as the passage of time.
In the you-didn’t-ask-but-I’m-going-to-tell-you-anyway department, imagine that a 2D item having mass resisting the expansion of the ballon and that other things near that mass want to fall into the dent made by the mass. Now, you have a reasonable model for gravitation and time slowing down near heavy objects. Something having the mass of a black hole would resist the expansion completely – time would stop at the surface of the black hole.
There’s more but I think this is a good start.
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