Crash course as I understand it:
As you approach the speed of light, energy (energy of movement) converts to mass. So you will never reach the speed of light, but you will be getting heavier and heavier.
Apparently mass has something to do with gravity and time, so you literally become so heavy as you get faster, that time is warped (like a black hole). The theory is that time will pass much faster for you when you are in this state than people at a fixed location.
Or, the entire theory is wrong, which some people have made arguements for.