Plain English Meaning
The fastest speed, expressed as a fraction of the speed of sound, that the airplane is allowed to fly. Going faster than this risks airflow problems over the wings that the airplane was never designed or tested to handle.
Full Definition
The highest Mach number at which an airplane is certified to be operated. Mach number is the airplane's true airspeed expressed as a fraction of the local speed of sound, so an MMO of 0.84 means the airplane is approved to fly up to 84% of the speed of sound. At higher altitudes, where the speed of sound is lower and compressibility effects become significant, MMO replaces VMO (the maximum operating airspeed in knots) as the limiting speed.
Context Anchor
Seen in the airplane flight manual or , especially for operated at higher altitudes.