The Dúnedain (singular: Dúnadan) were the the Men of Númenor and their descendants who peopled Arnor and Gondor in the Second and Third Ages. Some of them fled Númenor just before its destruction with Elendil and his sons, while others had settled around the haven of Pelargir before the Downfall. They are also called the Men of the West and the Men of Westernesse (direct translations of the Sindarin term).
After the fall of Arnor and then Arthedain, some of the northern Dúnedain became the Rangers of the North. The surviving Dúnedainic population of Arnor retreated to the Angle south of Rivendell. In the mean time the southern Dúnedain, the Men of Gondor, intermarried more and more with so-called Middle Men, except in some regions (such as Dol Amroth).
The Westron name for Dúnadan was simply Adûn, "westerner", but this name was seldom used.
This name was reserved to those Númenóreans who were friendly to the Elves: the other, hostile survivors of the Downfall were known as the Black Númenóreans.