The Kobo site has three lists for your library. "I'm Reading" is what is on the device, "Purchased" is the books you have bought and "Trash" for anything deleted from either of the other lists. Books that are archived are in the "I'm Reading" list, so maybe I should say it is the books the device knows about.
If you delete a book from the device, or desktop app, the book is removed from the "I'm Reading" list, but left in the "Purchased" list. To get it back, select the book in the "Purchased" list and press the "Bookmark" button at the top of the list. The next sync to the device will put it back on the device.
The archive option in the desktop application is there when the device is connected., but it doesn't use the term "archive". There is an icon on each book showing whether it is on the device or not. Clicking on the icon or right clicking will give the option to remove the book from the device.