TMJ is short for Temporomandibular Joint. It is a joint which connects your lower jaw to the rest of your face (i.e skull). It looks something like this:

Surrounding this joint are some very strong muscles, some of which you can see in the picture above, some in the picture below:

Those two big muscles you can see, one coming from the temples down into the joint and one from the lower border of the lower jaw (the mandible) up towards the joint, those two muscles are the common culprits of most of our non-teeth related (non-odontogenic) pain! 
Do me a favour: make sure no one is watching you (or you may get called to the boss’s office for a “little chat”), open your mouth, put your pointer finger inside your mouth and your thumb on the outside of your cheek. Now close your teeth together (without biting your finger, please) and clench a bit. Can you feel a “ridge” forming between your fingers as you clench? Follow that ridge up and down as far as you can and feel the width of it. That is your Masseter, the strongest muscle in your body (based on its weight). This muscle is one of the “muscles of mastication” (chewing muscle). It can close the teeth with a force as great as 90.7 kilograms (on the molars). Masseter is closely associated with the Temporalis. To find this one, put your hands on your temples and open and close your mouth. Then there is the Lateral Pterygoid Muscle, this little two-headed muscle is the only muscle responsible for opening your mouth, when working as a pair with the same muscle on the other side. When it works alone on one side only, it helps move your jaw to one side. The Medial Pterygoid Muscle assist with chewing and moving your jaw forward and to the side. 
So, next time you are at a dinner party, impress everyone with a little dental anatomy trivia you picked up here today!