They give you a token, you do a GET request to browserid.org with it and get the user's email, that's all. The user has to register their email with browserid.org first.
Wasn't one of the benefits that you don't need to rely on a third party service?
I believe you will definately rely on one (of many possible) 3rd parties.
The third-party service handles the case where the user's browser doesn't handle BrowserID natively, which makes it possible to adopt this service without waiting for user's browsers to catch up.