Plain English Meaning
The fastest you should normally fly. You can go a bit faster than this, but only when the air is smooth, and only carefully. Hitting a strong gust above this speed could damage the airplane.
Full Definition
VNO is the maximum speed at which an aircraft may be operated in smooth air. Above this speed, the airplane should only be flown in smooth air, and then only with caution. On the airspeed indicator, VNO is marked as the upper end of the green arc, where the yellow caution arc begins.
Context Anchor
Seen on the airspeed indicator as the top end of the green arc and the beginning of the yellow arc.
Derivation
The 'V' stands for velocity, and 'NO' stands for 'normal operation.' So VNO is the velocity for the top of normal operation — fly faster than this and you've left the normal operating range and entered the .