It’s an Archive button for Mail, and you can guess what it does. Instead of having to mess around with filing messages into folders, a single click will throw them into the archive. It even comes with its own ready-made keyboard shortcut (Command+Option+S), to make archiving even faster and easier.
When you need to find something specific, use Mail’s own search, which is quite up to the task of hunting through enormous archives (I’ve used Mail in this way, as a backup for my Gmail account, for years now).
If you need Mail to be a little more flexible, try Mail Act-On, which we mentioned back in number 8 in this series.