Social influence report - the description is vague, I know! Also since the reboot of the community many of the old links to your answers are no longer there which can be frustrating.
This report is generated when you use/add social buttons featured in the Marketo social suite to allow leads to share your content.
For example, if you put the Facebook, linkedIn, and Twitter button(s) from Marketo into a newsletter page, that report can spit how how many people shared this content via those channels, and how many unique leads (i.e. not in your database) it generated. There are a few other reports that can happen when these features are leveraged, let me know if you have any questions!
Amanda Scigaj is right. Details for Social Influence report are not available in Product Docs https://docs.marketo.com/display/public/DOCS/Report+Types. This report enables you to review social activities generated, and track how often your leads tell/refer their friends about you.
Dusty Garner-Carpenter or Steven Schaefer - any ETA on when documentation will be available that talks about some of the enhanced social capabilities in Marketo? I realize some already exists - but for those of us that purchased the social add-on capabilities, we find that comprehensive documentation is lacking - in this case, the social influence report.