Interest-rate risk is the risk, taken by bond investors, that interest rates will rise after they buy. Stated another way, it is the risk that a bond's yield will rise (as its price falls) after it has been purchased.
All bonds involve interest-rate risk, but some involve more than others. The more interest-rate risk a bond involves, the more its price will fall as its yield rises. Duration quantifies the amount of interest-rate risk a bond involves.
Generally speaking, long-term bonds involve more interest-rate risk than short-term ones do.
And generally speaking, bonds with small coupons -- that is, bond that don't involve much credit risk -- involve more interest rate risk than bonds of the same maturity
with large coupons. A rise in interest rates hurts more if you're earning only 5% a year in coupon income than if you're earning 10% a year.