What are the small boxes at the bottom of the Mail App?

Having updated to iPadOS15, you have now encountered the “Shelf” - this being a new feature of the now revised iPadOS multitasking environment. 

iPadOS multitasking permits you to run multiple “instances” of the same App, such as Mail - with each instance, perhaps having a different open inbox, mail message or draft.

For example, if you have three running instances of Mail, tapping the icon you describe will open the shelf with three thumbnails - each corresponding to each running instance of Mail. Simply tapping a thumbnail will switch directly to that running instance of the Mail App.  Swiping a thumbnail off the top of the screen closes the respective view.

This article from Appleinsider has a useful explanation of this new feature along with many of the updates to multitasking:

https://appleinsider.com/articles/21/08/12/how-to-master-multitasking-on-ipad-and-ipad-pro-in-ipados-15

Another useful resource:

Use multitasking on your iPad - Apple Support

The iPad User Guide is available both online using a web browser (such as Safari), or as an Apple Books download:

iPad User Guide - Apple Support

https://books.apple.com/book/id1567104892

Hi, lartcon,

Thanks for stopping by the Apple Support Communities. Based on what you've described, it sounds like you may be referencing an option related to multitasking. You can get more information on this feature here: Use multitasking on your iPad - Apple Support.

The feature in question will allow you to access multiple email mailboxes at once. Looking at the Mail sidebar, there should be two squares overlaying one another in the bottom right. If you tap this button, it should engage the screen you are referencing.

If this does not answer your question, don't hesitate to respond back.

Best!