It has to do with the gravitational pull of the sun and moon, their position relative to each other, and the fact that our bodies are 70% water. If the moon is going to affect the sea, of course it's going to affect me.
A full moon is the time when tides are the most extreme, when many things are at their most extreme, including human behavior. It is said that we have the tendency to be headstrong during a full moon, and are less likely to listen to the needs of our bodies, thus more likely to injure ourselves.
At the new moon, we tend to be more grounded and calm, but also less inclined to exert ourselves, or generally tired, so you can see how that might affect a yoga practice.
There it is. Simple enough, I suppose.
Apparently, the lunar cycle also has an effect on gardening: "The Farmers Almanac recommends planting seeds at the new moon when the rooting force is strongest and transplanting at the full moon when the flowering force is strongest."
I say all this, think about all this, because it's incredibly mysterious and fantastical to me to think that the moon and the movement of the moon has so much to do with how we feel, how we act, how much energy we have. It reminds me of something I read one time, about the Santa Ana winds and how people in California act differently when the winds come, behave in a bizarre manner, and it's mostly due to the winds (I think it was Los Angeles Notebook by Joan Didion - I really want to read that again). I can't quite put my finger on why these things intrigue me so. It's mysterious and magical, and we get to be part of it. We get to move with the moon, sit with the sun, and learn the secrets of the universe.
Another conversation for another day is the coinciding of the lunar cycle with a woman's cycle. I may be having that conversation with myself, but I'm interested to know why they coincided when people were living outside, and can we make them coincide again if we're more in tune with and pay more attention to the cycle of the moon.
My former English professors bid me cite my source: ashtangayogacenter.com/moon