When the terms premium and discount are used in reference to bonds. they are telling investors that the purchase price of the bond is either above or below its par value. For example, if a bond with a par value of $1,000 is selling at a premium when it can be bought for more than $1,000 and is selling at a discount when it can be bought for less than $1,000.
Bonds can be sold for more and less than their par values because of changing interest rates. Like most fixed-income securities. bonds are highly correlated to interest rates. When interest rates go up, a bond's market price will fall and vice versa.
To better explain this, let's look at an example. Imagine that the market interest rate is 3% today and you just purchased a bond paying a 5% coupon with a face value of $1,000. If interest
rates go down by 1% from the time of your purchase, you will be able to sell the bond for a profit (or a premium). This is because the bond is now paying more than the market rate (because the coupon is 5%). The spread used to be 2% (5%-3%), but it's now increased to 3% (5%-2%). This is a simplified way of looking at a bond's price, as many other factors are involved; however, it does show the general relationship between bonds and interest rates.
As for the attractiveness of the investment, you can't determine whether a bond is a good investment solely based on whether it is selling at a premium or a discount. Many other factors should affect this decision, such as the expectation of interest rates and the credit worthiness of the bond itself.
For more on bonds, check out our Bond Basics tutorial.