The game takes place in the year of 1968, and revolves around Lincoln Clay, a biracial orphan and Vietnam veteran. As an orphan, he was constantly looking for a family, until he joins the armed forces and fights in the Vietnam War. He returns to New Orleans, after the war and he joins "The Black Mob". After surviving a murder attempt by the Italian Mob, Clay attempts to start his own criminal organization and get revenge.
Source: Wikipedia, "Mafia III", available under the CC-BY-SA License.