The open date is the date and time when you first allow the students to view and work on the problems. If no opening date is set, problems are not viewable. You can set a general opening date for the whole course (your domain coordinator might have done this for you), and then your problems become available immediately after importing them. Particularly cloned courses may have an opening date already, which may be in the past.
Note that "Open Date" only controls access to problems. Webpages, PDF-files, etc, are treated differently than problems: they are viewable by default, but access can be limited by "Content Opening Date" and "Content Closing Date."