Definition
A designated paved area near the departure end of the runway where pilots stop the airplane to perform the before-takeoff engine run-up and final checks. The position is oriented and located so that propeller blast does not blow loose debris toward other aircraft, hangars, or people, and so the airplane is clear of taxiways and the runway itself.
Plain English
A marked spot near the runway where you park the plane to do your final engine checks before taking off, positioned so your propeller wash doesn't blow stones or dirt onto anyone behind you.
Context Anchor
Used during the before-takeoff check, after taxiing from parking and before entering the runway for departure.
Derivation
Run-up' refers to running the engine up to a higher RPM to test it. The 'position' is simply the place where this is done -- a specific, planned spot rather than wherever the airplane happens to be.
Why Pilots Care
Using the proper location keeps propeller blast and debris from damaging other aircraft or interfering with runway operations while confirming the engine is ready for flight.
Intuition Check
Do not assume a run-up position is the same as the runway entrance or the hold-short line. It is the safe place selected for checks before takeoff, and it may be in a marked run-up area or another suitable spot assigned or allowed by the airport layout.
Example Sentence 1
After taxiing clear of the ramp, the pilot pulled into the run-up position and angled the nose away from the parked aircraft behind them.
Example Sentence 2
Airport diagrams show the run-up position so pilots know exactly where to complete their before-takeoff checks without blocking traffic.