Reinvestment risk is the risk of investing the proceeds of called call bonds at lower rates and the investment, in the case of plain vanilla bonds, of coupon interest at lower rates than the assumed reinvestment rate.
The bond pricing formula assumes that the coupons received are invested at the rate paid for the bond, i.e. this is an important assumption of the formula. However, this is not certain, and the rate may be lower. It is for this reason that certain investors favour zero coupon bonds.