A set of instructions given to the model by whoever built the application, sitting above and before anything the user types. It defines the model’s role, tone, limits and available information. Users generally never see it, and it explains much of why the same underlying model behaves quite differently across different products.
Technical view
Usually a distinct message role that models are trained to weight more heavily than user turns, though the separation is a matter of training rather than a hard architectural boundary, which is why prompt injection and instruction-override attacks remain possible. System prompts occupy context on every request, making them a natural target for prompt caching.
Related
Part of AI Terminology Index, section: Controlling and Extending Behaviour at Run Time.