The message appears when you try to open an eBook on multiple computers PCs or multiple devices with different Adobe IDs. That This is not possible. All devices must be authorized with the same Adobe ID.
How to enable Adobe Digital Editions with an Adobe ID:
Adobe Digital Editions is now authorized with your Adobe ID. Repeat this process on any computer that you intend to use for eBooks. If ADE is already authorized and you want to change or delete the authorization, read here: Deauthorize Adobe Digital Editions.
Furthermore check if your mobile devices have been correctly authorized with your Adobe ID:
It may be occur that already borrowed eBooks are no longer usable until the end of the loan period, as they were not correctly authorized with your ID. To test whether it works, you should borrow and download a new eBook.