Exactly the archive feature that's on desktop, although for me it's not very important to be able to archive locally on mobile; archiving on my mail server is fine.
For the interface, perhaps swipe to select and then hit an archive button. Although swipe to archive is implemented in many mobile email clients, and I archive email much more than I explicitly mark it as un/read.
In the unified inbox, I'd expext that achiving would archive relative to the inbox for each mail.