Just as the name implies, if something goes sideways during the processing of this particular preference, it will abandon ship and stop processing midway through. For example, if your preference is trying to make contact with a particular server (for a drive mapping, file copy, or something of that nature) and can't reach the server, by default the preference would continue with applying the rest of its settings, but checking this box tells Group Policy to bail if any errors are encountered.
Keep in mind that other preference packages or policies that exist in the GPO will continue to work and apply to the workstation; the selection to Stop processing upon error only pertains to the ...
