I use "webmail" to refer to a remote hosted web interface. GMail, Yahoo Mail, Hotmail, riseup.net, etc. This is the dominant way that people access email, and it's not possible to secure well because of the "webapp crypto problem."
Mailpile, on the other hand, is a locally hosted MUA that happens to use your web browser as the UI. I think it's a great idea, leveraging the UI properties of a web browser, but with everything running locally.
All development of a new secure email protocol has been stymied for the past 13 years by webmail. It is not possible to provide end-to-end encryption if you don't perform that encryption on the client side, and in the webmail world there is no "client."
I'm excited about Mailpile because it could be what gives us a usable local MUA, which is the precondition to deploying a nice, modern, usable, end-to-end encryption protocol.