The Dunedain are the vaguely Elven but mostly man type of Man who are the rightful leaders of men (democracy doesn;t come into it in Middle-Earth). When their Realm was based in Numenor they were more commonly called Numenoreans, since they had more than one Realm the collective term for them became simply Dunadain.
They were the descendants of the Peredhil (Half-Elves), specifically Elros (brother of Elrond). They were the Kings of Numenor throughout the second Age, until Iluvatar did some funky stuff and wiped Numenor off the face of Ea when Ar-Pharazon sailed to Valinor to conquor the Blessed Realm (he was brainwashed by Sauron). Elendil had brought many of the Numenoreans (faithful to the Valar) to Middle-Earth, and they started up Arnor and Gondor. But then the whole thing with the Last alliance comes into it, and Elendil dies, Isildur gets the Ring, and so on. After some odd number of generations, the line of Kings from Isildur breaks, and his heirs founded Arthedain, its capital Fornost. However, the Witch-King, in command of Angmar, is able to take the capital and scatter the Dunedain. Thus they became the Rangers of the North, of whom Aragorn was the Chieftan prior to Sauron's defeat at the end of the Third Age. Among Arnor and Gondor, the blood of the Dunedain mingled with that of lesser Men, and they became thus short-lived as they once were. Only with the Rangers did the Bloodline hold, and Aragorn lived to be something around 250 years old. And considering that he was 80 or 90 during LotR, he was pretty youthful for his age.