Universal manhood suffrage is the principle that every adult male citizen is entitled to vote. In the United States, it was always assumed that this did not apply to slaves and the legal fiction that Indian tribes are sovereign nations kept the franchise away from them as well. The process of extending voting rights to non-whites and women are dealt with under civil rights and women's suffrage.
At the time the nation was founded, universal manhood suffrage was not the rule in any state. The usual qualification for voting was property. Two complementary arguments supported this: first that men of property would be best qualified to rule, and second that men without property could not be trusted.