The WordPress Server hosts contains user management, product subscription, and Single Sign-On (SS0) service for the applications. When you access an application from apps.socialsql.com, it will authenticate with the SSO service and check if the user has registered to access the particular application.
Web Application Server
The Web Application Server hosts the web applications such as the SocialSQL Facebook app. In the case of that application, it also interacts with Facebook's servers via their APIs when fetching data to be indexed.
The Data Server holds the persistent data for the web applications and is not for use with the WordPress applications. Hence, there is no communication between the WordPress server and the Data Server. For the SocialSQL Facebook app, data fetched from Facebook is stored and indexed in the database to facilitate subsequent searches. A local customised search engine resides here.