The numbers inside a model — often billions of them — tuned during training. Everything the model "knows" lives in them. Training sets them; inference uses them unchanged. Also called weights.
Mechanically, the parameters are what turn input into output. Next-token prediction is a giant calculation: the tokens in the context window go in, get multiplied through the parameters, and a prediction for the next token comes out. There is no database of facts inside the model, no code lookup table — just these numbers, arranged so that the calculation tends to produce useful output. Facts the model can recite from training, like a standard library API, are parametric knowledge: stored in the parameters, not retrieved from anywhere.
The detail worth internalising is that parameters are frozen after training. Nothing you do in a session changes them — no correction you make, no codebase you show it, no mistake it learns from. Every session runs on the same numbers. This is why the model is stateless, why its built-in knowledge stops at the knowledge cutoff, and why anything project-specific has to arrive via context instead. The only way parameters change is more training — which produces, in effect, a different model.
Usage:
"Can we fine-tune it on our codebase?"
"That'd update the parameters — different model afterwards. For one project it's almost always cheaper to load the codebase as context than to retrain."