What is the meaning of convexity?

convexity is a measure of the sensitivity of duration to changes in yield levels. Convexity is a measure of the stability or instability of the measured duration over a range of yields. If convexity is low, that is, if the price/yield relationship is close to a straight line, duration is stable. If convexity is high, duration is unstable. The greater an instrument's convexity, the less accurate duration will be. See: duration, effective duration, Macaulay duration, and modified duration.