Help:CentralAuth
The "Login successful" page appears when you have successfully logged in to Wikipedia. On the same page, you may also see a row of icons for other Wikimedia sites. They are to show you that you have also been automatically logged in to those sites by means of unified login. You can reveal the name of the site for each icon by hovering over it. Clicking the icon will do nothing.
If Wikipedia was unable to log you in to one of the other sites, then the corresponding icon will not appear. It may simply be absent or replaced with text.
Automatic login requires you to accept third-party cookies. If you have disabled third-party cookies, automatic login will not work, regardless of the success message.