Negative convexity is the idea that as interest rates decrease they get to a certain point where the value of certain bonds (bonds with negative convexity) will start to increase in value at a decreasing rate.

Interest rate risk is the risk of having to reinvest at rates that are lower than what an investor is currently receiving.

Mortgage backed securities (MBS) may have negative convexity because when interest rates fall mortgage owners will refinance for lower rates, thus prepaying the outstanding principle and increasing the interest rate risk that investors of MBS may incur.

Callable bonds are similar to MBS because of the possibility that the principle is being returned to the investor sooner than expected if the bond is called causing a higher level of interest rate risk.