Passage of time,the of speed light, and Reletivity

On almost every Discovery networks, History Channel, Or PBS show I see about outer space, they almost always go over relativity and light speed. They say that time is relative to the observer, and thy use the same stupid analogy on every show. "Spaceman Bob goes the speed of light for one year, comes back, and earth has aged 50 years" .......then they stop explaining why and say "Because time is relative, see?" Then they move on. Thats not a very good answer if you ask me. Leaving me on my couch, swearing at my TV. It's an example of relativity, sure, but one that opens the door for other questions. I also saw a segment on a show(I think it was The Universe w/ Stephen Hawking on Sci channel) and they were talking to a guy that works at a detection station for particles that enter the earths atmosphere but get (destroyed/evaporate) within a thousandth of a second.(I don't think it was wimps) So, if they get destroyed so fast they would all be in the upper atmosphere and undetectable on the surface. But this guy shows that his detector is getting hits from these particles, and he says that it's because they're traveling at the speed of light, so time goes slower for them, so they decay slower......something along those lines. I like this example alot better. I understand the concept of relativity.(not the math) I understand that as you approach the speed of light time slows down.(I think) But what I don't understand is what speed has to do with the space-time continuum. I don't know why time slows down for spaceman bob. I know that space-time can be warped by gravity/mass, but by speed as well? Can someone shed some light on this? How does speed affect the passage of time? Why does time seem to slow down? Archived source: https://web.archive.org/web/20101205120116/http://www.spacetimeandtheuniverse.com/general-physics/4542-passage-time-speed-light-reletivity.html