Traditionally, at least in the American context, it refers to a group of (mostly Jewish) intellectuals who, decades ago, migrated from the left to the right. They were "neoconservatives" because they were newly conservative, having previously been on the left. The prototypical example is Irving Kristol:
http://www.thedailybeast.com/articles/2013/06/05/neoconservative-needs-to-be-retired-why-not-try-imperialist.htmlHowever, since the 1990s, people started talking about a so-called second generation of neocons (like Irving Kristol's son, Bill), who adopted the same domestic political agenda as "regular" conservatives, but really only diverged on foreign policy, where they advocated a hawkish posture. Anyway, read that Peter Beinart column that I linked to, and you'll get the gist of it. This column might also be useful:
http://www.nationalreview.com/articles/206955/neoconservative-invention/jonah-goldberg