Look up the Hafele and Keating experiments with atomic clocks, some good information there.

Travelling at the speed of light would basically mean that it would be possible for astronauts to travel far into the future while aging very little. A crude way of looking at it would be seeing time and space as being represented by two different axis's on a graph. The steeper the line goes up up the speed axis, the less it moves along the time axis. A nearly vertical traveling line (representing the fastest we can travel) would mean next to no movement along the horizontal time axis.

Wish I were able to explain it better.