LLMs contain a LOT of parameters. But what's a parameter?

LLMs contain a LOT of parameters. They're the mysterious numbers that make your favorite AI models tick. What are they and what do they do? I am writing this because one of my editors woke up in the middle of the night and scribbled on a bedside notepad: "What is a parameter?" Unlike a lot of thoughts that hit at 4 a.m., it's a really good question--one that goes right to the heart of how large language models work. A large language model's parameters are often said to be the dials and levers that control how it behaves.