The separate password page is served over https instead of http like the initial page. This allows the initial page to load faster without the ssl handshake overhead while still sending the password over an encrypted connection.

What's unusual to me is that the username field is on the initial page. On most sites I've used that upgrade from http to https, only a generic login button is on the unencrypted page, e.g. creditkarma.com. Maybe facebook a/b tested this setup and found users log in more often.