@Lizelle2
Resonline is a channel manager system. http://www.resonline.com/resonline/
This is normally something a host would use when they have multiple listings on multiple sites. The system receives and manages bookings that a host gets from instant booking sites. Perhaps it is a business booking from a rep at that company in your town on business?
If the dates are grey in the calendar and you have not received a request to book, it usually means the system is waiting for guests to verify with proper ID or there is an issue with their payment method. We have had hurdles a couple of times with company credit cards so would not be too concerned about this. If the guest can't sort out whatever issue is keeping them from booking or requesting to book, the calendar should clear in 24 hours. I think most of the time they submit whatever the system is asking for and do wind up booking.
Hope that helps, Lisa