When you archive a project, it won't be displayed in the list of available projects when users are entering their work hours for the day. However, these projects will be available when logging time for dates prior to archiving them.
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 again.
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.
You can archive multiple projects in a single action by bulk selecting them and hitting the Edit button.