Muscle strength is what happens when the nervous system communicates a message to the muscle fibers to contract so as to produce force. Often the force produced by a muscle contraction is against resistance. Dumbells, theraband or tubing, or something heavy to lift or carry all qualify as resistance to muscle contraction.
The contracting of muscles (in a workout, for example) causes minute injuries to occur in the fibers of the muscles. The body sends a healing response to the "injured" area. After the healing takes place (usually within a period of several days), the muscles are actually stronger than they were before the workout (or other contraction).