Here is what I've found to be the most intuitive way to think about it: everything is always moving at the speed of light through spacetime. When you move through space you are not changing the magnitude of your velocity (through spacetime) at all, only the direction. So the faster you move through space, the slower you move through time. If your velocity through space is v (relative to some reference) then your velocity through time is sqrt(1-(v/c)^2) seconds (from your point of view) per second (from the point of view of the reference against which you are measuring your velocity through space). When v=c, then you are moving through time at zero seconds (from your point of view) per second (from any point of view moving at <c). So your time never advances. You get where you are going (and everywhere in between) at the same time that you left (from your point of view).