So, to the outside observer, light has traveled a bit further than 1 rocket ship length. Since the observer knows that it takes light 1 second to travel 1 rocket ship length, the observer measures the elapsed time for the event to be more than 1 second. He says that the clock in the rocket ship is running slow. The moral of the above story is that, due to relativity, time can slow down, as you measure it for other people. Now consider someone at the event horizon of a black hole.
Light travels away from that person at the speed of light.
The only explanation is that time must stop at the event horizon.