Kindles should automatically download and install the update if they're turned on and connected to Wi-Fi. But if they're not then the devices won't be able to connect to the internet and download new books.
Amazon has posted a notice online about the update and has also emailed affected users.
If you don't manage to update your Kindle by Tuesday then you'll see a message on screen that reads "Your Kindle is unable to connect at this time. Please make sure you are within wireless range and try again. If the problem persists, please restart your Kindle from the Menu in Settings and try again."
The only way to fix a Kindle that didn't receive the update is to connect it to a computer and manually install the update.
Here, via The Verge, is the list of Kindle devices affected:
- Kindle 1st Generation (2007)
- Kindle 2nd Generation (2009)
- Kindle DX 2nd Generation (2009)
- Kindle Keyboard 3rd Generation (2010)
- Kindle 4th Generation (2011)
- Kindle 5th Generation (2012)
- Kindle Touch 4th Generation (2011)
- Kindle Paperwhite 5th Generation (2012)