When you Archive a project, it won't be displayed in the list of available projects when users are entering their work hours. Any existing data and reports won't be affected.
Similarly, when you Unarchive a project, it'll be available for users to assign work hours to.
Admins can archive and unarchive any project. Non-admins will be able to do it for the projects they worked on if they have the right permissions in their Team Settings.