With regards to bonds payable, the term amortize means to systematically allocate the discount on bonds payable, the premium on bonds payable, and the bond issue costs to Interest Expense over the remaining life of the bonds. (Bonds are likely to mature in 10 years or more.)
The term amortize is conceptually similar to the term depreciate, except that depreciate is used when allocating the cost of a plant asset to expense.
Unless the discount, premium, and issue costs are insignificant, the amounts are to be spread to Interest Expense over the remaining life of the bond. The most precise way to amortize these is to use the effective interest rate method. A less precise method is the straight-line amortization method, which is often an acceptable alternative.