For those just tuning in, Google takes a unique approach to letting users read their own content in Google Play Books, one which is not shared by any other ebook vendor. In order to read a personal ebook in GPB on your Android device, Google requires that you first upload the ebook to their servers before downloading it again with the Google Play Books app. The upload feature is available in the iPad and iPhone apps, on the Google Play website, and in the GPB Android app.
If, for example, you find an ebook you wish to read at Feedbooks Google wants you to download it, upload it, and then download it again before you can read it. And yes, that is as strange as it sounds, and it is the main reason I have stayed with 3rd-party apps like Aldiko and Moon+ Reader when reading on Android tablets.
While I'm sure everyone can agree on the value of storing personal ebooks in the cloud, requiring that all of the ebooks be stored there is almost Vogon-ish. Wait, did I just prove Google made contact with extra-terrestrials?