The system is called Square, and the free app is available to download now for iPhone OS and Android. Basically, you fire up the app, attach the dongle, punch in the amount (say, whatever you agreed on for selling a couch on say Craigslist), and then have the buyer swipe their credit card through the adapter. No personal information is stored, and the buyer has to sign the phone with their finger. Once that happens, an SMS or email is sent to the buyer confirming the purchase.
It's a pretty simple solution, and it has the potential to revolutionize small business for whom it's quite difficult to get a proper credit card system setup, and the fees can be outrageous. With this, setup costs are essentially nothing, and the fee structure is much more reasonable.