Persona, the protocol, doesn't actually rely on your email account's password. It uses the domain from your email account to figure out how to authenticate you; if you want to use some other way than via your email, that's fine.
That’s just how their fallback provider works. BrowserID — the protocol — does not rely on email in any way. There’s no guarantee that if you have valid assertion for joe@dns.tld there’s also an email account by that name.
If you log out, that's the password you'll use to log in again. The login session is good for a while so you can continue to login with already-authenticated identities (and you can have as many as you want) on persona-enabled sites.
Thanks for clarifying. I was assuming that was the case but the login/creation page needs to have a graphic or a narrative talking about what it does and how the process works a bit more before it reaches a more public audience. As a software developer I had an idea of how the thing worked but it wasn't spelled out enough. I understand that it's beta but the whole thing is weakly documented from a user's standpoint as to why it should be trusted.