The closed box simply allows the user to flag that a voteCenter is closed (ie. no more ballots are expected). It is only really relevant to Manual Entry and Central Count vote centers since AccuVote-OS and AccuVote-TS vote centers are considered closed when all memory cards have been uploaded.
The closed flag allows GEMS to differentiate between precincts that have reports (ie at least one ballot has been counted in the votecenter for the precinct) and those that have completed counting. This is most relevant for central counted vcenters.
This status is displayed in the listview for reportunits and vcenters. It is also currently used for California export to determine the number of precincts reporting.