Plain English Meaning
The one instrument the pilot watches most closely to see whether the nose is in the right position for what they are trying to do. Which instrument that is depends on the maneuver.
Full Definition
The instrument that gives the most direct indication of the aircraft's pitch attitude for the maneuver being flown. In straight-and-level flight at a constant altitude, the altimeter is the primary pitch instrument because it shows immediately whether the nose is holding the altitude. The primary pitch instrument changes depending on the maneuver — for example, in a constant-airspeed climb, the airspeed indicator becomes the primary pitch instrument.