When you Archive an Article, the content is put into a state which removes it from your site as published content. The Article is still available from within the Control Panel and can be retrieved for editing or republishing purposes. Trashed Articles are just one step from being permanently deleted but are still available until you Remove them from the Trash Manager. You should use Archive if you consider an Article important, but not current. Trash should be used when you want to delete the content entirely from your site and from future search results.
What is the difference between Archiving and Trashing an Article?