Plain English Meaning
It's how hot the burned gases are when they exit the engine. Pilots watch this number to fine-tune how much fuel the engine is using compared to air.
Full Definition
The temperature of the exhaust gases as they leave the engine's cylinders, measured by a probe (thermocouple) placed in the exhaust stream. EGT is used as a reference for adjusting the fuel-air mixture, because the temperature of the burned gases changes predictably as the mixture is leaned or enriched.
Context Anchor
You will see EGT on engine instruments, especially during cruise power settings, mixture adjustment, and engine monitoring.
Derivation
“Exhaust” comes from older words meaning “to draw out” or “empty out.” In an engine, exhaust is the burned being carried out after . That makes the reading of the gases leaving the engine.