What does time has to do with the velocity of light?

Dan B's answer is pure drivel. Traveling backward in time (if we could travel faster than light) has NOTHING to do with "catching up to the light to see it again." Please take a physics course before answering physics questions.

In any case, the reason why time slows down as you move faster has no reason. It just does. It is an observed fact. So yes, if you flew around in a spaceship at close to light speed for a while, you would age very slowly. So what might be for you only a few minutes would be years on earth. When you returned to earth, years would have gone by. This is the only sense that you can travel into the future.

You can never travel into the future because future events haven't happened yet. However, it is possible (in theory) to travel back into the past. Everything we observe is reflected light. So if we can travel in the direction of light at a speed that is faster than the speed of light, we can catch up and pass the reflected light of the event, then see the event happen again.

It's much like firing a bullet from a gun. Let's say you have the eyes of an eagle and the speed of a falcon. You are down range of the gun and "see" the bullet pass you by. You go speeding further down range and pass the bullet. Turn around and you can see the bullet again as it passes you by. You can never see the bullet until AFTER is is fired (time passed).