In
baseball, a slow breaking pitch that curves slightly to the left when thrown by a right-hander, and drops dramatically. The curveball is thrown by snapping the elbow to generate transverse spin in the direction of the curve.
Sandy Koufax may have had the greatest curveball ever.
In colloqual speech, "curveball" is used to describe a surprising event, usually one that affects pre-made plans. To "throw someone a curveball" is to tell them something unpleasant they were not expecting to hear.