An update to the Google+ Photos app on Chrome OS enables the app to automatically backup your photos to Google+ when you import them, even when the app isn't actively running. Previously you had to manually launch the Google+ Photos app to initiate an import when you connected a phone, USB drive or SDcard, but now that can all happen in the background.
When an automatic import is completed you'll receive a notification indicating that the photos are ready to share. You can also check progress of the upload by launching the app, and pause the upload at any time if you choose to do have it start again at a different time.
The app should automatically update on your Chrome OS device when you have a connection, and you can always check to see if you have the latest version by comparing it to what's available in the Chrome Web Store. The latest version with Google+ automatic backup is 1.288.0.