The basic idea of Inbox is to offer a more productive version of an email client. Rather than simply being a list of messages and conversations, Inbox understands that there is a lot more to be done with email. With that in mind, Inbox gathers your reminders, allows you to pin messages with reminders attached, automatically bring back messages that you don't want to deal with right away, and take contextual actions on certain messages.
Mailbox, then you will be familiar with everything found in Inbox. First of all, the app is an extension of the current iteration of Gmail, which has the automatic labels for Social, Promotions, Updates, and Forums. Inbox takes the next logical step with that functionality and includes preset "bundles" for Travel, Purchases, Finance, Social, Updates, Forums, and Promos. And, it also includes the option for you to create your own "bundle", which essentially acts like an uber-label above what you may already have in your Gmail. You can manually remove or add messages to bundles, in order to teach system how you want the categories to work.If you've used Gmail, Google Now, and
Then, Inbox sprinkles in some Google Now functionality that everyone loves, and mixes it with the functionality that you'll find with Mailbox or the Boomerang extension for Gmail. Those features are mostly centered around making your mail work for you. This means being able to "snooze" a message for a certain amount of time (like you can with Mailbox or Boomerang), but with the added functionality of being able to "snooze" a message until you reach a certain location. So, if you don't have time to deal with something right away, you can procrastinate, but you'll be held accountable once the timer lapses or you reach the set place. Or, you can simply "pin" a message and that will be stored along with your reminders in a sort of "to do" list.
The Google Now functionality is shown with the reminders options, where the reminders you set based on time or location will show in Inbox; and, it also shows with the contextual options available for travel and calendar messages. This means that if you have an email for an upcoming flight, you might get the option to check in for that flight, or track the flight, if it is already in process. Plus, you'll get quick buttons to track a package from a shipping email, or the yes/no/maybe toggles for a calendar event.
All of this is awesome functionality must be applauded; but, at the same time, it is hard to figure why this needed to be a separate app. If Google had rolled it out incrementally, it all feels like functionality that could have been pushed into the Gmail app without issue. You start with the expanded auto labels, which are easy enough to implement compared to what Google had already done with Gmail.
Beyond that, you've got the features from Mailbox/Boomerang, which means swiping right to left to "snooze" a message. Currently in Gmail, no matter which way you swipe, it will either archive or delete, depending on your settings. With Inbox, you swipe left-to-right to archive (marked as "Done" in Inbox) and right-to-left to "snooze". This is the classic case of added functionality, but only necessary if that functionality helps you in your day-to-day life. Some people will love the option to have a message bounce back, but others will have no use for that.
Overall, though, I'd expect that most people would find at least some use for Inbox compared to Gmail. The UI is definitely different, and takes a bit of getting used to, but once you get past that, it is an app that will help you be more productive on a daily basis compared to your usual generic email/gmail app. Overall, I'd expect that this could have been pushed as a straight Gmail update, but the full feature list might have been too much for some casual users. Rolled out slowly, it might have been okay for the general public, but taken all at once it is a bit more than you might expect in a single update.
To be honest though, there are pieces that would be too much for someone on a first shot. It is a whole new UI, separated day by day; it gives more of each message compared to each Gmail line; and, of course, it will mix in reminders as well. You'll have to deal with "Done" meaning "Archive", and a whole new "bundle" set of categories, but that's about it. On a smaller set, Google has fixed the hamburger menu to let you swipe through your "bundles" and labels, but still have essentials like "settings" on the bottom. Although, depending on how many labels you already have in your Gmail, that hamburger menu list can be very long. There are also a couple of odd missing features, like a "select all" option in the web version. At the end of the day, it is a matter of if you need the extra functionality or not. If so, Inbox will definitely add useful features for you. If not, then you're probably best to stick with the Gmail app that exists already for Android and iOS.
This could very well be the beginning of the next phase of email. I was in on the initial launch of Google Wave, which was originally touted as the future of email; and, while it was as exciting on the feature side, it wasn't as cohesive and connected as Inbox was overall. Google Wave was a mess of interesting features, but never came together properly, which eventually led to its end, and the features of Wave being dispersed between Docs, Hangouts, and Gmail. This time around, Google has taken a more conservative approach in tackling the next evolution of email. The attempt this time isn't as ambitious, but is more realistic. Wave pushed too far, but Inbox is pushing just enough. It isn't quite a revolution in email, but it is definitely an evolution based on how email currently works; and, it's a worthwhile upgrade for many.