The comments on this video thread are actually pretty fascinating and add a lot.

Commenter Khaz says:

My problem with grasping this is that these people say movement affects time, how do they know that? All they do is show a photon clock which is basically just a representation of time. An object moving but is not in fact TIME itself. Just because a representation of time slows down it doesnt mean time slows down. A second is always a second no matter where you are how fast you are going… what my brain. I’ve watched endless explanations but still dont get it. Doomed being stupid forever? Is there an explanation for why time is diluted by movement?

Commenter V Kiosk has a fascinating reply:

time dilation is proven because if we assume that the speed of light is constant, time dilation would be necessary to avoid contradictions. If you were on a theoretical spaceship travelling at 99 percent the speed of light, which is impossible but lets just theorise, and fired light in the direction we were moving, from someone watching the ship, the light would appear to move at the speed of light relative to them. But to the people on the ship it would only look like the light is moving very slowly. This is similar to if you threw a ball while driving, to a person looking at you from outside, the ball would look faster than what you perceive. This shouldnt be allowed because the speed of light relative to non accelerating objects is constant. To solve this time dilation comes into play. This paradox would be solved if we assumed that time for objects moving was slower, so seemingly slow motion would actually be extremely fast. Its like looking at a sports car in slo mo. it looks slow, but the time is also slow so in reality it is moving very fast. Time dilation is a product of a paradox which can only be solved if time dilation existed. Hope you understood.

That is an earful but fascinating none the less.

We hope you enjoy the video and feel free to comment with your ideas!

thanks to pbs.org for the great info