Plain English Meaning
The speed the pilot holds the airplane at while climbing after takeoff. Different climb speeds are used depending on whether the pilot wants to gain altitude quickly, clear an obstacle, or simply climb comfortably while the engine stays cool.
Full Definition
The airspeed at which an airplane is flown during a sustained climb after liftoff, selected to give a desired combination of climb performance, engine cooling, forward visibility, and safety margin above stall. Specific published climb speeds include Vy (best rate of climb, the speed that gains the most altitude per unit of time) and Vx (best angle of climb, the speed that gains the most altitude per unit of horizontal distance).