A coupon is a detachable ticket or certificate
redeemable for some benefit.
The term originally rose to prominence in the context of finance, as a means of expediting interest payments on bonds. Each bond certificate would have a given number of coupons attached, each of which would be redeemed at the stated time for the interest due. Though modern bonds do not make use of actual physical coupons, the terminology remains, giving us terms like "coupon payments" for periodic interest payments, "coupon rate" for annual yield, and "Zero Coupon Bond" for a bond which yields only a single payment at maturity.
In modern usage, "coupon" most commonly refers to those used in retail promotions. Advertisements in magazines, newspapers (especially the unavoidable FSI), supermarket circulars and direct mailings will often include detachable coupons which can be redeemed, with the purchase of a certain product or combination of products, for some benefit, typically a discount or another item free. These discounts or bonuses tend not to be of very large value, usually around fifty cents to a dollar on purchases of five dollars or less, and are either absorbed by the retailer or refunded in whole or part by the manufacturer, depending on who initiated the promotion. If businesses employ promotional discounts of higher value, they usually take the form not of discounts at point of sale but rather of mail-in "rebates".
This negligible value generally limits the coupon as a promotional strategy to an attempt to overcome competing brand loyalty (either to product or retailer), rather than to induce consumers to purchase something they would not otherwise. As such, it tends to be employed more often on "staple" commodities like basic foodstuffs. It also means that those "coupon clippers" who regularly use multiple coupons per shopping excursion are apt to be derided as poor, elderly, or eccentric, apparently placing a low value on the productive time they use in searching out and gathering coupons.
In addition to the obvious promotional effects, a benefit of coupons that most consumers might overlook is that they allow sellers to judge the efficacy of their advertisements. Each coupon is encoded in such a way that manufacturers or retailers can determine where the consumer originally found it. By comparing the numbers of coupons returned, advertisers can determine the effect of an advertising campaign, compare the relative strength of particular appeals or tactics in selected markets prior to widespread roll-out, and determine in which channels to concentrate their advertising buys for maximum return on expenditure.