Plain English Meaning
The slowest speed the airplane can fly while still doing what the pilot tells it to do. Any slower, and it stalls.
Full Definition
The slowest speed at which an airplane can be flown under full control, just above the stall, where any further reduction in airspeed or increase in angle of attack would cause an immediate stall. At this speed the airplane is fully responsive to the controls, but only just — small mishandling will cause loss of control or a stall.
Context Anchor
Seen in short-field approach and landing discussions, where the pilot may need to fly slowly but must not get so slow that control is reduced or lost.
Derivation
Minimum comes from a Latin word meaning “smallest” or “least.” Controllable means able to be controlled. Together, the phrase points to the least airspeed at which the airplane still remains under the pilot’s control.