Genesis connector is part of Web Analytics package of Campaign.
Using this connector you can share offline kpis between Campaign and Adobe Analytics.
Also it will allow you to enrich the tracking formula in a way to have Analytics specific data added to each tracked link for onle tracking of information over a website or landing page also running with Analytics.
This will help you determine how many visitors on website came through your email and then get their cart abandonement and other information inside campaign to use them for re-targeting.
I could not find any references to "Adobe Genesis" or relationship between "Adobe Genesis" and "Adobe Analytics" in the official documentation. The documentation only refers to "Web Analytics" and "Web Analytics" is a very broad term.
Particularly these lines from the documentation are ambiguous. On reading the below lines one would think that Adobe Genesis is another Product from Adobe. But only after reading your post above, I can conclude that it is refering to Adobe Analytics.
The words "Web Analytics" can be changed to "Adobe Analytics"
"The Adobe Genesis connector allows Adobe Campaign and Adobe Genesis interact."
"Using the Adobe Genesis connector, Adobe Campaign has a way of measuring internet audience (Web Analytics). "
Can you please let me know how can i receive data back from GA to ACC? I followed all the steps mentioned in our step by step process and our GA team has confirmed that they are receiving the data. Now how do I import that data back to campaign? Is there a way to integrate directly in GA, where there is a 2 way communication (receiving the data back from GA for re targeting)?
I believe there is additional option (standalone or needed w/ the Genesis option), you can schedule a technical workflow to extract the required campaign data elements on daily basis from Adobe campaign mart (system tables) to SFTP site or push the files to Analytics. Keep in mind that via Genesis connector, you will be able to transfer/share with Analytics the standard data elements. Any enriched data elements (attributes) you may have added in campaigns (e.g., campaign/segment metadata, snapshot attributes, etc.), you will need to extract those via flat file extract method to Analytics if required by reporting.
It all comes to the requirements and what is needed for reporting and analysis in Adobe Analytics.