This FIRST thing to remember is that you can only measure speed by comparing with something else. There is no such thing as the concept of "I am moving", but rather "relative to them I (or they, it's interchangeable) are/am moving".
Now when you compare speeds you can also compare clocks, and the same principle applies - you can only measure time by comparing to someone else.
I used to think about it as I explained in my previous comment. But now that ars is making these comments, it seems like I'm grasping something new.