As a consumer, my wife signed up for it and gets one email a day with a special deal from a local business. She's found some great deals that we've used and the merchant gets lots of volume.
As a merchant, you run a special price for something you sell (service, product, whatever) and then the revenue generated from it is split 50/50 with Groupon. Would you make more money at full price, sure! But you're also getting HUGE volume and getting your name out there. Not a bad option for a small and/or struggling business. The only other catch, other than the 50/50 split is that only about 1 in 8 applicants make the cut. The winners are usually already getting raves on sites like Yelp and Citysearch "and the deals must offer a substantial discount from normal prices and not be similar to other promotions regularly offered by the vendor".
If your business needs more business, check it out!