The central idea of Inbox is that your goal is INBOX ZERO, and that after dealing with any email, you swipe it to the side (or mark it as Done with the checkmark in the web UI) and _do not see it again_. (Like 'Archive' in Gmail.)

The second idea is that your emails are Bundled by category. This is similar to a tag or a filter, but you can choose to have them still show (as a bundle) in the inbox, rather than being filtered to not-seen oblivion. For example, I had one bundle for Pull Requests, another for Jira notifications. The app auto-categorizers things for Finances, Promos, etc, so many of the spam-like newsletters you get will end up bundled together. (Bundles default to only showing things that are not Done, unless you click a bundle's category on the left navigation bar.)

That doesn't sound very useful. What makes it useful is that you can archive/Done an entire category. All of those emails from TeeFury, Newegg, Amazon, Steam, Github, etc that you would normally consider usually-clutter suddenly are SUPER easy to deal with. It basically makes archiving those no longer annoying, as you can do it all at once. Best of all, you see them first, so it's harder to have something get filtered without being noticed.

Pinning prevents you from archiving an item (unless you explicitly click it). This means that you can ping something in a bundle, archive the bundle, and it will archive all the other things, and leave the bundle with that one item visible.

I am profoundly saddened that Inbox is going away. As others have said, it _changed my life_ in terms of how I dealt with overwhelming email volumes at work.