Think of it this way. Exercise places stress on your body. Exercise runs your body down. Exercise, in itself, doesn't do your body any good at all. It makes you feel tired, run down, lethargic, sore etc. BUT exercise does the wonderful thing of providing a stimulus for your body to recover.
Recovery initiates itself immediately after exercise when your body is so run down that it needs to repair and rebuild itself so it can handle the physical stress more effectively next time.
Recovery is a slow process. If your exercise session is intense enough, you can stimulate a recovery response for up to a week or more (depending upon the stimulus).
Your body can only handle so much physical stress through exercise. If you persist, your body will take measures to shut itself down. The first is fatigue which you will feel during exercise. From there, you may become light headed, dizzy etc. Then you may faint, dehydrate etc. If you continue to persist, that's when some serious medical complications can arise because the body isn't equipped to handle such extreme forms of physical stress.
Sleep is when a lot of your recovery occurs. As I said, it's a slow process, which is why you need so much of it!
You may be interested in signing up to our course, Conquering Your Body. Within one of the lessons, we discuss recovery in great detail.