I get the concept, I just don't understand specifics of how it happens. I'm thinking a possible exam question on my OS test would be something like "what is a system call and how does it work". I can answer the first part, but not the second part. And when you say "from the outside world" that sounds like... a hardware interrupt?
edit:
I just found something that I think will help: something called the "time quantum" and the timer interrupt handler for Linux. It says once the time quantum expires, the process gets preempted... which is something like what I'm looking for, so I think it'll yield some answers. Consider this solved for now, and thanks for the help Salem.