Parameters are the numbers a model learns. Training adjusts billions of them until the model produces useful output, and everything the model knows is stored in those values rather than in any database it can be shown. When a model is described as 8B, 200B or 1T, that is the count of these weights.
The count matters commercially because the whole model has to fit in memory to run at all. Processing speed is irrelevant if the weights do not fit, which is why memory capacity, not raw performance, is the number that decides whether a given machine can host a given model. Roughly speaking, a model needs about one byte of memory per parameter at common compression levels, so the arithmetic is easy to do before anyone quotes you hardware.
Bigger is not automatically better for a specific job. A well-chosen eight-billion-parameter model handling a narrow, well-defined task will often beat a frontier model on cost, latency and consistency, while losing badly on anything requiring broad reasoning. Match the parameter count to the task.