If your customers have to visit your locations in order to do business with you, you can request that they check-in on Google+ in order to redeem your offers. They can choose to share the check-in publicly or with some of their circles, which helps spread the word about your business on Google+. They can also choose to keep their check-in private and still redeem an offer.
If your customers do not have to visit your location, for example if you serve homes or businesses by delivery or by callouts, you can keep this option off (set to “No”) and customers will not be asked to check-in when they redeem offers. We use the Service Areas and Location Settings setting on your listing to determine if you have a service area for offers that have already been created. When you create new offers, you can choose whether to allow a check-in during redemption.
The option is not yet visible within the Places Offers tab. Google recently started purging the free Offers created in Places if they did not offer a real discount of some sort. Perhaps that was in anticipation of Google + integration of check-in.