Explained in layman's terms:
The faster you go, the bigger your mass becomes. At everyday speeds this effect is absolutely negligible, but at the speeds closer to the speed of light, it becomes more and more pronounced. It's one of the aspects of Einstein's theories of relativity (general and special). So, if you were moving at a speed a fraction away from the speed of light your mass would be almost infinite. You can't move at the speed of light because then your mass would
be infinite, and anything with infinite mass can't be moved. Light on the other hand has no mass, it's just energy (electromagnetic waves or photons) so it can and does move at the speed of light. Why are things this way? They just are, it's different from the things we see in everyday life, on the scales we live in, but it's true.
I'd just like to make it clear, that when I say "your mass increases", I don't mean just the feeling of weight (the way you feel heavier in an upwards accelerating elevator), but your actual mass increases (it becomes larger and larger, like the mass of a planet, and you become a stronger and stronger gravity source).
This is why spaceships in SF try to avoid this by using jump gates, warp, subspace or stuff like that.
Of course, if you know all of this yourself (you weren't clear on that), just ignore me, and read Christopher's post.