Derik,
Its an online based company that you can register your email address to, in order to receive 'daily deals' in your local area. There are normally between 1-4 deals per area every day. Every offer is at least 50% off normal price, and it can be anything from tooth whitening to nights in posh hotels to carpet cleaning.
The companies who offer the discounts also agree to pay groupon a set amount of each deal that is sold on their behalf (normally 50%). So in the example of the hotel room for a night, if normal price was £100, offer price would be £50 (or maybe less), and the hotel would expect to receive £25.
That's a very brief rundown, hope its starting to make some sense?
Ash