In recent years, it's been widely thought that social shares have an effect on organic rankings but any direct correlation has been hard to pin down. Articles with high social shares tend to rank well. Does this mean that social shares affect ranking? Google says no.
It isn't shares, it's engagement.
Engagement naturally leads to social shares. So, to be specific, it is the amount of shares that matters, it's the percentage of people that share something or like it after seeing it. (unique people who engage with article / unique people who saw the article)
Why?
The same emotions that get people to share and like things are the same emotions that get people to click on search results.
Moral of the story - Facebook Ads, Facebook's news feed, Google AdWords, and Google organic search are all guided by systems that reward remarkable engagement with greater visibility.
The more engaging your content is, the more likely it is to rank well.