A system prompt is the instruction an AI reads before it sees anything you say — the standing brief that sets its role, tone, and rules for the whole conversation. If a prompt is the question you ask, the system prompt is the job description the model is working under while it answers.
It is the difference between "an AI" and "your AI." A system prompt can say: you are a contracts paralegal, write in plain English, never invent a citation, always ask before assuming a jurisdiction. Every later message inherits those rules without you repeating them.
Why it matters at your desk. This is exactly what the "custom instructions" or project-level settings do in tools like Claude Projects and Cursor — you are writing a system prompt, even if the box is labelled something friendlier. Set it once and every draft, answer, or code suggestion comes back already shaped to your standards, which is far more reliable than re-explaining yourself in each chat.
What to watch for: the system prompt is powerful but not bulletproof. It strongly biases behaviour rather than guaranteeing it, so a rule like "never do X" reduces X without making it impossible — which is why genuinely high-stakes constraints belong in guardrails and human review, not just a sentence at the top.