Plain English Meaning
A takeoff where the wind is blowing partly from the side, so the pilot has to use the controls to stop the airplane drifting sideways or weathervaning into the wind while accelerating down the runway.
Full Definition
A takeoff performed when the wind has a component blowing across the runway rather than directly down it. The pilot uses aileron deflection into the wind and rudder as needed to keep the airplane tracking straight along the runway centerline during the takeoff roll, then transitions to a wind-correction angle (crab) after liftoff to maintain the desired ground track.