The app downloads books to your device memory that are added to "Read" and "Read later" sections by default. You'll have to purchase a subscription to read offline the books that are available for a prepaid subscription.
When you add a book to the "Read later" section by tapping the "+" icon, or start reading a book, it is automatically downloaded into the memory of your device. This process takes some time, so you'll have to try not to close the application. Just read for a little while, for example.
If you want to change the download settings of the app, please follow the links for more details: Android, iOS or Windows Phone.