A premium bond is a bond which trades above its par value. In other words, it can be said that it is a bond which costs more than its face value. A bond trades at premium when rate of interest on the bond is higher than the current rates in the market.
For example, a bond with a par value of $1,000 may trade at $1,150 or at a premium of $150. If the bond is to mature after 10 years then in such case it is tradable in the secondary market. Such a bond can be bought and sold before it gets matured after time span of ten years. If the bond is held till its date of maturity, the holder of the bond receives the par value of the bond which is $1,000 in the above mentioned example.