The maximum force of contraction exerted by a muscle is controlled by the Golgi tendon organ (GTO), which is a receptor found in the muscle-tendon unit whose function is to limit the tension developed by the muscle. If you did not have GTOs, you would be considerably stronger, but also at increased risk for ripping tendons from bone. When the GTO senses a tension that it considers to be dangerous, it causes a reflexive inhibition of muscle contraction (engineers might recognize this as being analogous to a negative feedback loop). In most people, though, the GTO is too sensitive and inhibits the muscle before there is any real danger of injury. As a result, strength is needlessly limited.
An interesting sidelight to this topic is that the GTO inhibition of strength can itself be inhibited. This is the primary means by which ordinary individuals can exhibit extraordinary strength in certain dire crises. For example, most people have heard of the case in which a mother lifted a car that had fallen on her son. There are several other stories, many of which are documented. The manner in which the GTO is inhibited is not known, but it must involve the central nervous system.
While there is no known conscious method of inhibiting the GTO to allow superhuman feats of strength to be performed at will, the GTO can be desensitized over time to allow some increase in strength independent of muscle growth. This is accomplished by performing jerky movements against resistance, performing the same or similar movement in which increased strength is desired. There is some attendant risk of straining muscles or tendons with this technique, and it is certainly not intended for beginners. For an advanced athlete looking for a competitive edge, it may be the difference between winning and losing, and thus may be worth the risk.
Although this should be fairly obvious, it is worth mentioning that strength increases resulting from GTO inhibition will do nothing to augment muscle size. Since most people who work out with weights do so for cosmetic reasons (i.e., to appear stronger or to lose weight), GTO inhibition is of no use to them.