To add to my comment: If you really want to understand relativistic time dilation, you want to understand the bouncing-light mirror-clock experiment. It's even

To add to my comment: If you really want to understand relativistic time dilation, you want to understand the bouncing-light mirror-clock experiment. It's even in the article. And it's not even an analogy, it's really why moving objects run slow. You can derive the exact special relativity time dilation factor from it.