The bond's price is the sum of the present value of every future cash flow (annual coupons, plus the face value at maturity), discounted at the market yield y:
Price = Σ CF_t / (1+y)^t
Macaulay duration is the present-value-weighted average time to receive those cash flows; modified duration divides it by (1+y) to give an approximate % price change per 1 percentage-point yield move. Convexity captures the curvature the straight-line duration estimate misses:
%ΔPrice ≈ −ModDur·Δy + ½·Convexity·Δy²
Because the true price-yield relationship is convex (bowed, not straight), the duration-only estimate always understates the price at both higher and lower yields — adding the convexity term closes most of that gap.