Plain English Meaning
The spinning wheel inside the instrument has been knocked off its proper axis. While in this state, the instrument can't be trusted and needs to be reset before it shows accurate information again.
Full Definition
A condition in which a gyroscopic instrument's gyro has exceeded its mechanical limits of rotation, causing it to spin off its normal axis and lose the stable reference it was providing. Once tumbled, the instrument displays unreliable or wildly incorrect indications until it is reset or allowed to re-erect.
Context Anchor
Seen in discussions of attitude indicators, especially older mechanical instruments and unusual attitudes that can exceed the instrument’s limits.
Derivation
From the everyday word 'tumble,' meaning to fall or uncontrollably. The gyro literally tumbles off its axis when its limits are exceeded -- the -English image matches the mechanical .