The discount on non-amortized bonds is the difference between the nominal value of the bond and the amount actually paid for it by investors, i.e. the proceeds received by the bond issuer.
The issuer of the bonds amortizes, i.e. gradually writes off, the discount on the bonds over the remaining term of the respective bond as an interest expense. The amount of the bond discount that has not yet been written off is the discount on the unamortised bonds.
The downside or discount on an unamortized bond is the unamortized premium on a bond that comes into play when a bond sells for more than its face value.