I am a big fan of "hard sci fi" fiction even though I'll probably never be a scientist or engineer in my lifetime. So, I need help understanding a concept, in layman's terms, that keeps getting brought up in the books I like to read:

Let's say a space ship travels at light speed for about a year. By the time it gets to its destination, the people at that destination will have aged many decades while the people on board the space ship will have only aged a year. Why is that?