Hello - In a nutsheel the Connector does the following;
4. Integrated Search - THe Connector plug-in can allow for having a unfied search that searches across Lithium and SFDC Content (Solutions, KB and Library content
5. Lastly - SFDC Contact and Case records are enriched by Community data that show the Community attributes along with recent activity history
Hope this helps!
I have some high level process maps i can share if you want? or are you after the sfdc db schema showing the community objects? We are currently working on the integration between sfdc and lithium, working very well however we do have some issues we are working out such as any updates back from the community after you have posted a reply from sfdc dont get back into sfdc also your community user db is synced with sfdc every 24hours. when working with the case escalation you need a community user to be in sfdc for the "case, contact, account" assignment to work if you escalate before the contact has sync you could get orphan records but you can reduce the sync to less than 24hours. Also if you have any custom fields on your profile record within the community you want passing into sfdc you will need to get lithium to expose them.
hopefully our lessons learnt will help you 🙂