Plain English Meaning
RNP 1 is a rule that says the aircraft's navigation system must keep it within one mile of the planned track almost all the time, and must warn the pilot if it can't.
Full Definition
A navigation specification requiring an aircraft to maintain its position within 1 nautical mile of the centerline of the intended flight path for at least 95 percent of the total flight time, with onboard performance monitoring and alerting if that accuracy cannot be met. RNP 1 is typically applied to terminal-area procedures such as departures, arrivals, and transitions.