Two spaceships are traveling together through the galaxy at close to the speed of light. Mounted on one ship is a laser that can fire pulses of light, and on the other, a mirror. The pilot of the first ship fires a pulse at the mirror, and watches as it is reflected back. A clock on board measures how long the round trip takes.
But now suppose that he does this as the ships are passing an observer on a nearby asteroid. According to relativity theory, this observer sees the pulse moving through space at exactly the same speed that the pilot does -- namely, the speed of light. But he also sees the pulse traveling a longer distance, because from his perspective, he must add the forward motion of the ships to the motion of the pulse between them. So he measures a longer time interval for the round trip than the pilot does, because he is watching the pulse go farther without going any faster. This effect is called time dilation: if one observer is moving with respect to another, each perceives that the other's time is flowing more slowly.