Plain English Meaning
On a plane with more than one engine, it's the engine that — if it quits — causes the worst handling and performance problems. Losing this particular engine is harder to deal with than losing any of the others.
Full Definition
On a multi-engine aircraft, the engine whose failure would most adversely affect the performance and handling qualities of the aircraft.
Context Anchor
Seen in multi-engine training, aircraft manuals, and emergency procedures for engine failure after takeoff, during climb, or in other high-workload situations.
Derivation
Critical' here comes from the Latin 'criticus', meaning decisive or crucial — a turning point. In aviation, it flags the engine whose loss creates the decisive handling problem, not just any engine failure.
Why Pilots Care
Failure of this engine requires the highest minimum control speed and demands immediate, precise to .