Why warm-up and cool-down? What will happen to me if I don't do it?

What is physically occurring in my body during warm-up and cool-down?

I have a very limited amount of workout time, as do many people. It would seem to make sense to optimize the duration and method of warming-up and cooling down to leave as much time as possible for the regular workout without incurring bad effects. Any suggestions on methods for warming-up and cooling-down as quickly as possible?

thanks!