NOTE: I received some down votes to my answer. So I have added evidence that supports my answer below.
You clench your teeth to raise your blood pressure. I'm fairly knowledgable about biomechanics of the spine, and stabilization of the spine has been researched extensively. I haven't seen a paper that specifically focuses on blood pressure as a component of spine stability, but I'm pretty sure that higher blood pressure makes your spine more stabile for the couple seconds that your executing a demanding movement. In the long run, obviously, higher blood pressure will end your life prematurely.
As for myself, I have had a bad history with my teeth, which I'm not going to bother you with here. Point is, the health of my teeth trumps whatever I'm doing at the gym. So I have never allowed myself to grit my teeth. Ever. Does that mean I have never lifted my maximum potential weight? Probably. But I'm just not willing to take any risks with my teeth. If you have an older parent who is losing their teeth, you know what I'm talking about.
Now, here is my evidence for this theory. Hang with me because this is going to be a slightly long explanation. This paper shows that when tennis players grunt they hit faster balls. How does grunting increase ball speed? The answer is that grunting stiffens your spine. I quote from this paper: "Grunting appears to increase intra-abdominal pressure during the respiratory cycle, thereby increasing stiffness of the lumbar vertebrae providing greater trunk stability and increasing force development."
I would argue that, if you increase your blood pressure, this will also increase increase intra-abdominal pressure. Thereby, an increase in blood pressure will contribute to spine stiffness. Now, when you contract any muscle in your body, this contributes to your overall blood pressure. This is why, when the doctor measures your blood pressure, they ask you to relax every part of your body and to uncross your ankles and arms, and so on. Hence, clenching your jaw, even though it isn't a big muscle, will slightly increase your the blood pressure. If you don't believe me on this, clench your jaw the next time your doctor measures your blood pressure.
In summary, clenching your jaw increase blood pressure, and thereby increases inter-abdominal pressure, and thereby increases spine stiffness, and thereby gives you a more efficient force production.