I had this misunderstanding also, but if I understand it correctly...
Basically a site using Persona tries to send you to your email provider to authenticate. If your email provider is running Persona, you'll authenticate through them, and the email provider sends a token back confirming your identity.
Mozilla is the default identity provider for people whose email providers don't run Persona (yet). Once the project gains widespread adoption, Mozilla won't be processing much if any authentications because they'll be distributed to email providers.
Also it will in theory work as a browser extension, so your email provider sends your browser the token, and your browser sends the token to the websites you log in to. So your email provider doesn't know where you're logging in.
Basically a site using Persona tries to send you to your email provider to authenticate. If your email provider is running Persona, you'll authenticate through them, and the email provider sends a token back confirming your identity.
Mozilla is the default identity provider for people whose email providers don't run Persona (yet). Once the project gains widespread adoption, Mozilla won't be processing much if any authentications because they'll be distributed to email providers.
Also it will in theory work as a browser extension, so your email provider sends your browser the token, and your browser sends the token to the websites you log in to. So your email provider doesn't know where you're logging in.