If the market rate or yield rate is higher than the coupon rate on the bond, you would not purchase that bond at a premium because it is valued under market, so you'd purchase it at a discount.
Here's one way to look at it: Let's say you have two bonds and you are deciding which one to purchase. They both have face values of $2,000 (which means that when the bond period is up, you will receive that face value of $2,000). Bond 1 will give you a coupon rate of 6.5%. Bond 2 will give you a coupon rate of 8%. They both are selling for $2,000 and they both are 5 year bonds. Which one would you purchase?
Bond 1: Interest = $650 ($2,000 x 0.065 x 5)
Bond 2: Interest = $800 ($2,000 x 0.080 x 5)
You would make more money from Bond 2 so what would be the motivation for anyone to buy Bond 1? This is where discounting and premiums come into play. In order to make that bond marketable and appealing to purchase, the price you buy it for would have to be discounted (or reduced). Otherwise, no one would ever purchase it because they could just go find a bond with a better interest rate for the same price.
This helps to conceptualize it better. Market rates are forever fluctuating and it would be very cumbersome for bond issuers to keep changing the coupon rates on the bonds just to keep up with the market rate. So premiums and discounting are ways to help solve that issue.
I hope this helps!