If you login to a website such as security.stackexchange.com via OpenID, the website will use yadis/xrds to discover the identity provider based on the information entered by the user.
The website may need to redirect the user to the discovered login page of the identity provider, unless he is already logged into his identity provider and has told it to automatically accept login requests from the website. The yadis/xrds-discovery itself is not visible to the user, but of course he will end up at the right website (if everyone plays nice and does not attempt to phish for accounts)
In the end the website will use the discovered information to verify the identity and may retrieve additional information about the user.
You can find more information in the OpenID specification.