However, they have given small tests, like testing grip strength, and then electrically stimulated the muscles and tested again, and found that people exhibit about 25% more strength under electroshock, which definitely verifies people are in general stronger than they're normally able to access. Additionally, you may have heard of people being flung across an entire room after being electrocuted. This isn't because of the electricity - electricity doesn't move things like that - its because the shock caused massive muscle contraction, and the people flung themselves across the room, jumping far further than they would have believed possible under normal circumstances.
So, because they can't test hysterical strength, we can only hypothesize why adrenaline causes it. More than likely it is because your muscles are under several inhibitory systems, including pain as well as the neurological restriction of simply having not enough signaling at any given time to activate all the muscle fibers in a group. Strength isn't just about raw strength, its about timing; you need one perfectly timed electrical burst to signal all fibers to work in concert when exerting force. The more fibers activated simultaneously, the more strength you'll have.
Adrenaline most likely acts to remove several different limiter systems. Your pain sensation is dulled or removed entirely, your blood vessels are dialated and your muscles are more heavily oxygenated, and your neural activity increases; more brain activity = increased signaling, which means you're better able to activate more muscle fibers at once.
The reason we can't do this all the time is fairly obvious - it puts much more strain on the body and consumes far more energy. Since our bodies evolved in times of scarcity, our bodies evolved a logical mechanism for limiting the bodies ability to use its full strength and energy; only when the brain sensed certain stimuli (a tiger, a child in trouble), would it release its natural chemicals that overrode its own internal limiters, allowing for a brief state of higher muscle performance.
Thought I'd throw this out there just 'cause: what people normally call "adrenaline" is actually called "epinephrine". The name "adrenaline" comes from a company that tried to patent a synthetic epinephrine compound, and then name stuck. There's another hormone called "norepinephrine", which some scientists theorize may actually be responsible for "hysterical strength". It operates much faster than epinephrine, and acts as a primer, which engages the body and officially switches it to "fight or flight" mode. It can also cause the muscles to start dumping their glucose stores (your muscles store glucose for quick, instant feats of anaerobic strength, because aerobic energy doesn't engage instantly). The fact that norepinephrine greatly increases brain activity, and causes a massive release of muscular energy, may be the contributing factor to huge bursts of extra-natural strength.
Some people have (correctly) indicated that "adrenalin(e)" and "epinephrine" are called different things in different countries. True! I mostly included the edit to point out that the common reactions of the body to adrenaline / epinephrine in the case of hysterical strength can actually be attributed to several molecules, and refer to "epinephrine" so that it can be seen in relation to "norepinephrine." I would just add that the "proper" name for the molecule is still under debate, and this site does an excellent job summarizing the conflicting nomenclatures and debating for a unified name:
The brain controls muscles by sending impulses to "motor units", which is a motor neuron and the various actual muscle fibers that are activated by that neuron. This is called recruitment. If you want to curl a 20lb dumbell, your brain has to "recruit" all the proper motor units in your arm, hand, and shoulder necessary to lift it, by sending the "contract" signal to them. Humans have many, many motor units, which allows us for very intricate, refined movements. You can play guitar, dextrously use tools, and figure skate!
But it also means your brain has to work a lot harder, and disperse signals a lot farther and wider, to fully activate a muscle. Comparatively, chimps have much fewer motor units, but the motor units they do have control many more fibers. So a single "contract" signal now applies to a MUCH wider group of muscles, which makes them appear stronger.
No one is precisely sure, but on a given basis, for a given task for a large muscle like your bicep, you may only use as little as 25% of the total muscle fibers. Even though it seems like you're trying your hardest, your brain simply isn't signalling all of the fibers inside that muscle.
But lets take a scenario of hysterical strength. Adrenalin and norepinephrine activate your sympathetic nervous system, dialate your eyes, increase brain activity, and more importantly, consolidate your focus. If you think about lifting a dumbell in a gym, your concentration is branching out in many directions. You're thinking about your day, your surroundings, your hunger, aches and pains. All of these detract from your brains ability to send recruitment signals to motor units. But now, in a state of supremely focused motivation - rescue a loved one - all your focus is dedicated to a single task. NOW when your brain sends a recruitment signal, its sending it to MANY more motor units - 80, 90, maybe even 100% of the total muscle fibers in a given muscle, across many muscles.
In the moment, this may seem like superhuman strength, but in actuality, its only because we so rarely experience the full extent of our strength. Athletes get to where they are by practicing specific and timed recruitment of specific motor units. This study:
Shows that in athletes, the physical volume of their cerebellum (the part of the brain responsible for sending the coordination & motor recruitment signals) is larger than non-athletes; i.e, they can recruit more motor units, faster, while in a "normal" state than the average person. By contrast, in a high-stress adrenal state, your brain has to divert processing power to recruiting motor neurons in order to achieve your greater state of strength, compromising things like external focus, logic, etc. Athletes, because of a greater volume in their cerebellum, can achieve physically profound feats without compromising these functions, and don't need to rely on a sudden huge influx of Adrenalin to do so - they can summon it at will.Source