In debt instruments, a discount means selling below par value. A discount bond has no coupon at all: an investor buys it at a lower price and receives the full par value at maturity, with the difference representing their entire income. A promissory note placed with a discount operates on the same principle.
A coupon bond can also trade at a discount. This happens when market rates rise after issuance: the price reduction compensates the new buyer for an insufficient coupon and brings the yield to market level.
In a broader sense, discount refers to any reduction from calculated or fair value. For example, a company's shares may trade at a discount to book value or to valuations of comparable issuers.
General rule of interpretation: a discount is always justified by something. It reflects either higher rates, increased risk, or low liquidity. Purchasing "at a discount" in itself creates no benefit—it is important to understand why the market demands this discount.