Plain English Meaning
The hottest the engine's exhaust gets as you slowly lean the fuel mixture. Once you find that hottest point, you use it as a reference to set the mixture for cruise.
Full Definition
The highest exhaust gas temperature reached as the fuel/air mixture is leaned. As the mixture is leaned from rich toward lean, EGT rises, reaches a maximum value (peak EGT), and then begins to fall as the mixture becomes too lean to burn efficiently. Peak EGT corresponds to the mixture setting where combustion is most complete, and is used as a reference point for setting cruise mixture either at peak, rich of peak, or lean of peak according to the manufacturer's instructions.
Context Anchor
Seen when leaning the mixture in cruise and when using cruise performance charts that engine settings based on peak EGT.