Plain English Meaning
Turning off an engine on purpose during flight because something looks wrong with it, rather than waiting for it to break down on its own.
Full Definition
The deliberate, pilot-initiated stopping of an engine in flight when indications such as abnormal temperatures, pressures, vibration, or other warning signs suggest that continued operation could lead to engine damage, fire, or complete failure. The shutdown is performed before the engine fails on its own, while the pilot still has time to manage the airplane in a controlled manner.
Context Anchor
Seen in engine failure and abnormal engine operation discussions, especially when deciding whether to keep a troubled engine running or shut it down before it causes a bigger problem.
Derivation
"Precautionary" comes from the Latin praecautio, meaning "taking care beforehand." The term reflects the idea: the pilot acts in advance of an actual failure, not in to one.