Occlusal guards protect the teeth by evenly distributing the bite forces, and by introducing a sacrificial element for absorption of the bite stress besides tooth structure. They protect the jaw joints (TMJs) from damage, and the jaw muscles from tenderness and pain by reducing the amount of force the closing muscles are able to generate.
How do occlusal guards reduce muscle forces?
If your jaw joints don't already hurt, and your front teeth are not heavily restored with fillings, crowns, etc., you can try this simple experiment:
Place a tongue depressor (sucker stick) between your upper a incisor teeth (the front four). Make sure that only your four front upper and lower teeth (the "incisors") can touch the stick. Slowly and carefully, start to contract your jaw muscles to squeeze down on the stick. Stop immediately if you feel any pain. Now remove the stick and close your teeth fully together. Again begin to clench your jaw muscles. You should notice that you can develop a lot more muscle contraction force without the stick in between your front teeth than you can with it in there. It may help to place your fingers over the muscles at the corners of your jaws—you'll be able to feel more of them contracting when your back teeth can touch.
What you have just observed is a phenomenon called "proprioception" (or "nociception"), a feedback mechanism from the nerves that surround your incisor teeth, to your brain, that tells your brain not to let your jaw muscles squeeze too hard. A similar feedback mechanism is what gives you the ability to stand up and maintain your balance, only that proprioception system involves your leg muscles and nerves.
Occlusal guards help to reduce muscle contraction forces by placing the front teeth in function the way you just did.