The definition of a coupon: A form of payment just as cash, credit, debit, EBT, and checks are..
Bing definition is : Voucher redeemed by a store or company: a voucher that entitles somebody to a discount, refund, or gift, typically issued as a sales promotion
Why do companies do this? Well the answer to that is one of many the easy answer that everyone likes to hear is they like to do it when they change packaging launch a new product but the answer really is something I found in an article that most people really wouldn't like to hear especially if they don't use coupons.... here is some stuff from wiki
Coupons can be used to research the price sensitivity of different groups
of buyers (by sending out coupons with different dollar values to different groups). In addition, it is generally assumed that buyers who take the effort to collect and use coupons are more price sensitive than those who do not. Therefore, the posted price paid by price-insensitive buyers can be increased, while using coupon discounts to maintain the price for price-sensitive buyers (who would not buy at a higher price). When these coupons are entered at the time of the checkout process, it reduces the order total for the customer.
def this whole wiki is a good read for all of it go here