Groupon itself is a free service for customer to join. Each day, Groupon will send an email announcement to its subscribers, describing the deal-of-the-day in that metro area. Commonly, the deals are 50% discounts at a particular restaurant, or 50% discounts at a particular store. If we like the deal-of-the-day, then we purchase an electronic coupon directly from Groupon using our credit card or PayPal account. Print that coupon, take it to the restaurant or store, and redeem it for commonly double the value we paid.
Groupon is a commission-based middleman service. They provide a motivated customer base to the seller, and promises to achieve X number of sales per day. If Groupon doesn't meet that promised quota, there is no need for the seller to provide any discount services, nor any commission pay to Groupon. Much more common, however, is where Groupon exceeds their quota of daily interested customers, and then all of the Groupon customers enjoy a half-price deal while the seller enjoys a big rush of new customers, and Groupon earns a commission from the sales. (As of this writing, Groupon earns a commission of 50% of the coupon sell price). It's a very powerful win-win situation for all 3 parties.
Groupon is very popular for two reasons. Firstly, its subscribers are modern consumers who love to spend money. They especially love to spend money where they get a discount or a perceived bargain. Groupon works because it provides motivating choices for its motivated group of consumers.