I'm not sure, but the OP may be referring to books keeping their current page, bookmarks, and notes in sync.
I can't address how reliable this is myself. I rarely read on anything but the iPad these days. I will say it probably depends heavily on whether all devices have an internet connection, how often, and how reliably.
For instance, you may not be able to start reading where you left of on a second device if it does not have an internet connection when you first open the app. Likewise if you last read the book on the other device when you were offline.
The Kindle app can only sync when it is open and the device is online. If you consistently do your reading when there is no internet available, then the syncing will be erratic.