Open flying refers to flight sequences that have no pilot assigned to them. If I am a lineholder and have recurrent training in December and they have to remove me from a trip that trip will show up in "Open Time" and might wind up being crewed by a Reserve FO. Trips pop up in open time for all sorts of reasons like pilots calling in sick, not being able to get to the airport in time for the flight, Vacation, Training, etc etc.

As a reserve pilot you have access to our company system that allows you to view what trips are "open."