I believe this screen shows up when a very long distance is travelled and the user logs in via a different ip. Here are the two cases I have encountered.
2500 miles Montreal,Qc,Canada to Trinidad and Tobago,Caribbean
I was helping my sibling (in Trinidad and Tobago) with a problem on Facebook from Montreal,QC by logging into his account.
2300 miles approx Montreal,Qc,Canada to Portland,OR USA
Visited a friend and logged in via his computer.
So with these two cases I believe its based on time/distance between places. If I log in at place X but then log in to place Y only Z minutes after (first case) miles away (second case) then I receive the verification process. This only works on the initial log in. Any activity that follows seems to be okay for me.
You can see the most recent activity information in your settings under Account security. In this tab it shows information for activity of users (under the assumption that all users are yourself under different locations/IP) that have logged in successfully and accessed your page.