This never made any sense to me whatsoever.
I’ve see all the physicists (Michio Kaku, Stephen Hawking, Neil DeGrasse Tyson, etc.) explain this principle but it doesn’t make sense. They say that if you were to go to the moon and back at a certain speed near the speed of light, you might return to Earth a thousand years into the future like what happened in Planet of the Apes. But if you were going at the speed of light, you would arrive at the time light takes to arrive there. Why the dip? What is being missed?
Just want to add that what the person on the ship observes is length contraction. When their ship is at near light speed, the distance to their destination contracts to nearly zero (because it is moving at near light speed relative to them); this is why the trip seems short to them.