When adding a new project only the name is required. You can always visit the projects 'Settings' and change the projects settings.
An archived project is a project which is totally closed. They are only saved for historical purpose, and to ensure valid documentation if the company needs to look back. Archived projects will not be included in any statistics.
Templates can be cloned into new projects. When the project status is set to 'Template', it is moved away from the normal project view. It is advised, to remove any assigned users on templates, and only use templates for cloning to new projects - not for daily work.
For example: you created a project with tasks which is structured according to your company's standard - then set the status to 'Template'. When you need to create a new project according to your company's standard, just clone the template. You can at any time change a projects status to 'Template'.