Social metrics are taken directly from social sites public APIs to be shown at Ahrefs.
It is important to point out that we show social metrics for exact URL you enter (not for the domain as a whole).
For Facebook the number shown is the sum of: the number of likes of your URL, the number of shares of your URL, the number of likes and comments on stories of Facebook about your URL.
For Google+ that is the number of times the URL has been had the +1 button clicked, plus the number of times the URL has been shared/reshared on Google+, plus any +1 of those shares or comments.
For LinkedIn and Pinterest - amount of shares of your URL.