I can't order my photo book on my MacBook Air using the Photos app.

Apple stopped the print services completely. If you are running an old version of Photos - Photos 1 to 3, it will allow you to create books, but you cannot order them any longer. Upgrading the system to macOS 10.14 Mojave with Photos 4.0 will allow you to use third party project extensions as described by Rich. But Photos 4.0 does no longer support the creation of Apple Photos books at all, so you can no longer even create a PDF book to print yourself.

Since your book is ready for printing, I would simply save the PDF version of your book and upload it to Mimeo, Presto Photos, or any other service that can print Apple Books from PDF files. This is described here: Ordering Books and Calendars on a Mac that cannot be upgraded past El Capitan

• To save your finished PDF book as a PDF file (https://web.archive.org/web/20170614002828/https://support.apple.com/en-us/HT201504 or Check and review a project before you order using Photos on Mac - Apple Support) and then send it to a service that can print books from PDF files.
  • Mimeo used to print for Apple and can handle PDFs created in Photos, see: https://import.mimeophotos.com
  • Also Presto Photo can print from Apple https://www.prestophoto.com
  • If you are not located in the US, there may be local printing services, which would be more economic with respect to international shipping fees and shipping time. In Germany we can use photographerbook to print existing Apple PDF files: https://www.w2p-photographerbook.de/fotobuch-aus-aperture-iphoto-fotos

The Photos app is embedded in the operating system. To upgrade to a new Photos version requires upgrading to a new operating system. The current operating system is Mojave, with Photos 4. Apple no longer provides a Photo Book service. However, with Mojave and Photos 4 you can, from within the Photos app, click on File/Create/Book/App Store to get a list of photo book apps that you can download and use as extensions to create photo books. Then when you click on File/Create/Book the downloaded photo book app will show as an available extension that you can click on. Many people use Mimeo or Motif, but there are several other choices.

-- Rich