When you buy or sell bonds after the date they are issued, they trade on what's known as the secondary market, which is where most bond trading occurs. The corporation, government, or agency that issued the bond gets no income from these secondary trades as it does when it first issues the bonds in the primary market. But when the bond matures, the issuer repays the par value to the current owner.
If you buy in the secondary market, you may buy at par value, at a premium, or at a discount.
At a premium:
If you buy a bond at a premium, you'll pay more than the par value. Usually, bonds sell at a premium when their coupon rate is higher than the prevailing rate on similar bonds. Although you'll earn a higher rate, your yield will be lower than the bond's coupon rate since you paid more for the bond.
At a discount:
If you buy a bond at a discount, you'll pay less than par. The bond is likely to be paying an interest rate that's lower than the current rate. But your yield will be higher than the coupon rate since you paid less for the bond.