Plain English Meaning
The fastest the engine is allowed to keep spinning all day long without damaging itself.
Full Definition
The highest engine speed, expressed in revolutions per minute, at which an engine is approved to run continuously without time limit. Operating above this rpm is permitted only briefly under specific conditions (such as takeoff) if the engine is rated for it, and operating beyond redline is never permitted.
Context Anchor
Seen in fixed-pitch propeller discussions, power settings, tachometer markings, and the aircraft operating manual.
Derivation
Rpm means revolutions per minute: the number of full turns made in one minute. Continuous comes from a word meaning uninterrupted, which matters here because this limit is about a speed the engine may steadily, not a brief peak.