We all know that shares and likes metrics matter, at least for the developing and marketing teams. but is this important for users? Would it be better to have a simpler and clearer design for a blog for instance?, a design focused more on content than on sharing? or does showing the number of shares encourage users to actually share a post?
The importance of those numbers is directly related to Social Proof. It validates the quality and relevance of the content by showing other people's interest in it.
Quoting Smashing Mag:
This principle tells us that we like to observe other people’s behaviour to judge what’s normal, and then we copy it.
This article talks about this and other persuasion triggers: http://www.smashingmagazine.com/2010/11/persuasion-triggers-in-web-design/#trigger3
So in conclusion: yes, it is important for users, as it helps them choose what content is more reliable. Much like how upvotes and downvotes work on many sites, such as stackexchange.