As Jonathan Edwards wrote and presented his historic sermon "Sinners in the Hand of an Angry God", his emphasis was reformation. He was a British Reform Theologian who was preaching in the early 1700's, a time of discovery, exploration and revolution.
His emphasis was to encourage people to not depart too far from God and scripture in this exploration, discovery and revolution. This is a constant concern with theologians in any age.
"The natural men" that you ask about are people who live their lives according to strictly natural impulses, desires and plans. It describes one who has not accepted the spiritual guidance available from God that he has provided. In doing so, "the natural man" wanders without direction or understanding of what is truly important in life.
The emphasis of the sermon is that the tragedy of the natural man's rejection of God is to fall into "The Hands of an Angry God."