Plain English Meaning
How well the airplane can climb -- both how fast it gains altitude and how steeply it can go up. It depends on how much extra power and thrust the airplane has after just keeping itself flying level.
Full Definition
The airplane's ability to gain altitude, expressed as rate of climb (feet per minute) and angle of climb (altitude gained per unit of horizontal distance). Climb performance depends on excess power and excess thrust available beyond what is needed for level flight, and it is affected by weight, density altitude, airspeed, configuration, and bank angle.