Plain English Meaning
The runway length needed to get airborne and clear a set height above the ground after losing one engine during the takeoff. Because the aircraft accelerates more slowly on the remaining engine, this distance is longer than a normal all-engines takeoff distance.
Full Definition
The horizontal distance an aircraft requires to take off and reach a specified screen height above the runway surface when one engine has failed at or after the critical decision speed during the takeoff roll. For multi-engine aircraft operated under performance rules, this distance accounts for the reduced thrust available after the engine failure and is used to determine whether the is long enough to legally and safely depart.