Plain English Meaning
The airplane's nose is pointed noticeably up, higher than it would be in normal flying. If the pilot doesn't act, the airplane will slow down and could stall.
Full Definition
An aircraft attitude in which the longitudinal axis of the airplane is pitched up significantly above the horizon, beyond the pitch attitude normally used for cruise or climb. In recovery training, a nose-high attitude is one of the unusual attitudes that, if uncorrected, can lead to a stall as airspeed decays.
Context Anchor
You will see this term in recovery training, especially when correcting an unusual airplane position or preventing a stall.