What is the Moon, and why does it seem to change shape?

Look up on a clear night and there it is — the Moon, hanging in the dark like a silver coin someone forgot to put away. Some nights it's a fat round ball. Other nights it's just a thin sliver, like a fingernail clipping. So which is it? Plot twist: the Moon never actually changes shape at all. It only looks like it does, and the reason is genuinely delightful.
First, what even is the Moon? It's a giant ball of rock — about a quarter as wide as Earth — that loops around our planet again and again, like a faithful dog circling its owner. It's our closest neighbor in space, and it's been doing this same patient lap for billions of years. No fuel, no rest, just round and round.
