I'm still not sure why I received the email. My (two) Kindles are the 4th Generation Kindle Touch and both have the software version 5.3.7.3 (2715280002). According to the Kindle Touch Software Updates page, this is the up-to-date software version. The email text was as follows:
"Several of the Kindle e-readers registered to your account require an important software update. Update your devices to continue downloading e-books and using Kindle services.
To receive the update, follow these steps:
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Plug your Kindle in to charge during the update.
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Connect to Wi-Fi.
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From the Home screen of your Kindle, select Menu or tap the Menu icon. Then choose Sync and Check for Items.
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Leave your Kindle connected to both power and Wi-Fi overnight, or until the update is complete.
The software update will download and install automatically, even if your device is asleep. Your device may restart multiple times during the update process. You will get a final confirmation letter on your device when the update is complete.
If you do not update the devices’ software by March 22, 2016, you will no longer be able to access Kindle services or get the update via Wi-Fi. To resume access, you will need to manually update the software on each of your Kindle devices. Please visit our Help page for more details on how to update manually. "