Plain English Meaning
Every attitude indicator can only handle so much climb, dive, or roll before it stops working properly. The pitch and bank limits are the point past which the instrument can no longer be trusted to show what the aircraft is actually doing.
Full Definition
The maximum amount of nose-up/nose-down tilt (pitch) and left/right roll (bank) that an attitude indicator can accurately display before its internal gyro mechanism reaches a mechanical stop, tumbles, or otherwise fails to show a correct picture of the aircraft's attitude.
Context Anchor
Seen in attitude indicator discussions, especially when learning how far a gyroscopic attitude indicator can be trusted during steep or unusual aircraft positions.