Interest rate risk is the risk, taken by bond investors, that interest rates will rise after they buy. Interest rates and bond prices move in opposite directions. All else being equal, when interest rates rise, the value of a bond falls in value. Conversely, when interest rates fall, the value of a bond rises.
All bonds involve interest rate risk, and some involve more than others. The more interest rate risk a bond involves, the more its price will fall as its yield rises.
Lack of awareness of interest rate risk causes many investors to severely underestimate their total portfolio risk. For example, a retiree on a fixed budget may invest in a government bond fund because government bonds are generally considered to be some of the safest bonds in the world. However, the word "safe" here refers to their credit risk.
While long-term government bond funds have basically zero credit risk, they have a lot of interest rate risk. In fact, if interest rates rise by just 1%, the value of many long-term government bond funds will drop by 10% or more. Hardly the safest bond funds in the world when looked at from that standpoint.
When choosing the bond fund that is right for you, you want to find the best mix of total return and understand how much credit and interest rate risk the fund is taking to generate that return.