Although the site is currently in private beta, I've managed to get an account and take a look inside.
The concept is simple. Instead of just having a standard email address such as "email@example.com", using otherinbox you can create multiple inboxes on the fly such as "firstname.lastname@example.org".
This means you can have a separate email for all the different sites you use like email@example.com or firstname.lastname@example.org. Although with Gmail, and i'm sure other email apps, you can create folders, filters etc which all achieve the same goal. Of course being able to "make up" email addresses on the fly is a bonus.
The apps layout is good although its a bit to heavy and could benefit from some Gmail minimalistic touches.
I would also like to see a shortened domain. ie. instead of yourusername.otherinbox.com, try email@example.com etc.
You can help me test out OtherInbox by sending an email to firstname.lastname@example.org (but I won't be using this as a proper email client until it improves).