I'm not sure how many of the wise commenters here have actually used inbox - some of the comments kind of miss the point. I've been trying it out for a few months on my personal account.
From what I see, it basically does three things:
1. Automatically grouping emails. You can teach it how to group them. This absorbs the conversations like function that gmail and outlook have had for years. It's also a little more sophisticated than the tabs that gmail introduced a year or so back.
2. Focusing on action items - so making links and the like directly visable.
3. Sleep/snooze etc items. This is similar to flags, except they're a little more clever (e.g. only trigger when I'm at home or in the office next). These can be applied to individual items or to groups.
What it practically means is that if I order something from Amazon, it groups all the emails together and at a glance I can see the delivery status of my order and click directly on the tracking link (this is without opening the email). That's quite useful. (It doesn't, unfortunately, tell me how much tax I've avoided in the process). At the same time, the forum updates I signed up to to find whatever it is I've just bought and read all the reviews are quietly shuffled off to a separate group that I can look at when I have time.
The key here is that it's mostly automated and simplified. That is radically different from Outlook where I'd have to tell it to do all of that (e.g. to open the preview pane, create a filter) and would then apply the rules to all emails in quite a dumb way. I can enhance inbox - so I've long had a set of rules to label incoming email in gmail.
Now, I'm not actually defending inbox: I'm not totally convinced by it myself. My issue is that whilst it automates things, that automation is a little opaque and I'm not always sure that it's either right or good; sometimes dumb rules that I can write/understand/fix are better. The other issue is that it's not very good at hiding items once you've actioned them. So those Amazon orders remain front and centre until I hide the whole email. I'm also conscious that it means google is processing my inbox to make all these decisions, which might upset some people's sense of privacy.
The point is, it makes sense to critique/question inbox for what it is - not what it isn't. And what it is doing is quite a few steps ahead of outlook.