In fixed income
calculations, convexity estimates the amount duration
will change given a change in interest rates
Bond investors prefer bonds that have positive convexity. This is because when interest rates fall, the bond's duration increases, which makes the bond's price rise more. Conversely, when rates rise, the duration will shorten, and price losses will be less.
Bonds with embedded options (e.g. mortgage securities) have negative convexity. That is, duration extends as rates rise, and shortens as rates fall.