Muscles have to be exposed to more than they are used to handling if there is to be a positive change. Hopefully that is done in a safe manner. Confronted with a state of fatigue that is beyond what the body is used to, the body, as self-protection, will make a positive adaption by becoming stronger if given enough recovery time.
There are three stages of fatigue associated with resistance training. When you can no longer lift or move a weight you've reached concentric or positive failure. When you can no longer hold the weight you've reached static failure. This produces a deeper fatigue than positive failure. When you can no longer stop a weight from falling or lowering you've reached negative or eccentric failure. This is the deepest fatigue. Eccentric failure is best conducted with a trainer or spotter and on equipment where it can be safely performed.