If you're having difficulty downloading eBooks in the Barnes & Noble NOOK App for Android, try the following:
Refresh your library by going to the Library tab and swiping down and releasing once you see an icon of an arrow in a circle. This will sync your library to the cloud for any recent changes to your Library.
The payment method on your NOOK account may have expired. or in "Settings" on the NOOK Reading App for Android, and try downloading your books again. Access Settings > Shop & Purchases > Credit Cards
A default payment method may not have been selected for your NOOK account. then try downloading your books again.
If you're still having issues, move the item to the NOOK Cloud (also known as Archiving), and then try downloading your book again by tapping on the book cover. Items moved to the Cloud have a cloud symbol with an arrow on the cover.