The very short version is to think of everything being only ever able to move at the exact single speed c in a four-dimensional space, so whenever something wants to have velocity along a space axis, they need to trade off some from along the the time axis to keep the total velocity vector magnitude unchanged.
I like this way of thinking of it, so much simpler than the usual explanations.
I like this way of thinking of it, so much simpler than the usual explanations.