I'll try...

There seems to be a common misconception about time.  People often seem to think that you would be aware of time passing slowly at relativistic speeds - I mean to say that people think your conscious mind would still be working at the same speed as those back on Earth, while your body was going 'slowly'.  This is not the reality.

Time is a dimension, just as 'up/down', 'left/right' and 'forward/backward' are each a dimension.  Time is the 'future/past' dimension.  These are the four dimensions that make up our universe. So, we can travel up or down, left or right, forwards or backwards, and future-wards or past-wards (though we don't know how to do the latter).  We are all travelling forwards in time.  The future becomes the present which then becomes the past.

It's always difficult to talk about the passage of time, because we use a measurement of time itself to talk about time.  Time always passes at one second per second. But people in different places don't always agree with how much time has passed.  The passage of time is not uniform throughout the universe. 

Really, it comes down to the realisation that the speed of light (c) is a universal constant.  This means that the passage of time cannot be uniform.  Light has frequency (f), and it turns out that for speed of light to be a constant, time cannot be a constant.  Therefore, things travelling at different speeds experience time depending on their speed.  To show how this actually comes around requires a fair bit of equations and definitions.