(Think OpenID, but easier to use, easier to implement, and with better privacy protection.)
In brief: instead of a username and password at login, you get a user's email address and cryptographically signed assertion proving their ownership of that address. The assertions are ephemeral and scoped to your site, so once you verify it, you can set a session cookie and throw away the assertion. No more password column in your database, yet you still retain a direct relationship with your users.
Here's the underlying spec (working on getting it updated for Beta 1, but the principles are all there) https://github.com/mozilla/id-specs/blob/prod/browserid/inde...