Before you can read your books offline, you need to download the books when you are online. To do so:
Open the Google Play Books app when you are online. Move your mouse over the cover of books you'd like to download. Find the Make available offline checkbox in the pop-up that appears. If you are reading a title in the web reader, you can also access this option by clicking on the "i" in the right-hand corner of your screen
Once you select Make available offline for a title, the Google Play Books app will start downloading that book in the background. When this download is complete, the book is available for offline reading, and you'll see the gray text Available offline under the book cover.