Plain English Meaning
The height above the ground where, while you circle a point on the ground at a steady speed, your wingtip seems to stay locked onto that point without sliding ahead of it or behind it.
Full Definition
The specific altitude above the ground at which, when an airplane is flown in a level turn at a given groundspeed, a line extending from the pilot's eye through the wingtip appears to remain fixed on a point on the ground. It is calculated by squaring the groundspeed in knots and dividing by 11.3 (or by 15 if using miles per hour).
Context Anchor
Used during eights on pylons, where the pilot adjusts altitude as groundspeed changes around each pylon.
Derivation
From 'pivot' — to turn around a fixed point. The altitude is named for the way the airplane appears to pivot around the pylon on the ground when flown at exactly the height.