Plain English Meaning
The aircraft is flying at the speed of sound for the air it's currently flying in. Slower than this is below the speed of sound; faster is above it.
Full Definition
The speed at which an aircraft is moving through the surrounding air at exactly the local speed of sound. Mach 1.0 is not a fixed airspeed in knots — it varies with air temperature, so the true airspeed corresponding to Mach 1.0 changes with altitude and conditions.
Context Anchor
Seen in high-speed and high-altitude performance discussions, especially when comparing airplane speed to the speed of sound instead of to a fixed miles-per-hour value.
Derivation
Named after Ernst Mach, an Austrian physicist who studied how objects behave at and above the speed of sound. A is simply the aircraft's speed expressed as a of the local speed of sound — so Mach 1.0 means 'exactly the speed of sound,' Mach 0.8 means '80 percent of it,' and so on.