This just popped up on Twitter for me (I follow all the Google services), between now (or actually as of 2 hours ago) and 9 AM tomorrow PST anyone who emails email@example.com (from a Gmail address mind you) will automatically get an invite. Although it's fair to warn you that it might take some time for you to get yours. Originally, when Inbox was first unveiled and I signed up it took about two days for me to get mine. I know they also did something like this previously (as I wrote about it) and it took about a week for them to get to everyone who wrote in. So have patience, folks!
I wrote about Inbox before as well, with a quick "this is how it works" on it.
The succinct version is this. "Google Now + Gmail = Inbox. Except cards don't disappear." That's a quote from Pessimippopotamus by the way.
I will say this, Inbox isn't for everyone. If you've got Gmail setup just so with tabs and labels and all that it is very possible you won't like how Inbox handles your mail. I personally hate clutter (except on my desks) and that means I love seeing nothing in my email. Inbox lets me achieve that, it basically turns your email into a "to do" list. Reply to something and once that's done you can either "check" the item (which clears it from your Inbox, but doesn't delete it or anything like that) or if it's something you don't want to accidentally get rid of you can "pin it" (and it'll stay there despite any "done/checked" clicking you do) and so on and so forth.
If there's any questions about it feel free to ask. Myself and several other Odeckers have been using it for some time now. Personally, I think it's the bee's knees!
EDIT: Apologies to anyone who got a bounce back from the original email link. It should have been firstname.lastname@example.org. I accidentally wrote Gmail because that was the Twitter account I saw this linked from. My bad, everyone! Have a ferret as my way of apologizing!