Once the lending period for a Kindle Book ends, it will expire, returning it to the library. Expired titles cannot be opened, but you can remove them from your device.
If you're using a Kindle reading app, Kindle Fire, or Kindle Touch, tap and hold a title, then select Remove from Device. If you're using a non-touchscreen Kindle, push right on the directional pad, then select Remove from Device.
Once a Kindle Book has been removed from your device, you can also remove it from "Your Content" tab on the "Manage Your Contents & Devices" page. This removes the title from your "Archived" items the next time you sync.