Cusp meaning : A sharp point or pointed end. An important moment when a decision is made that will determine future events. A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point. A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture. A boundary between zodiacal signs and houses. Any of the pointed parts of a canine tooth or molar. A flap of a valve of a heart or blood vessel. To behave in a reckless or dangerous manner.