The Dúnedain (singular: Dúnadan) were the Men descended from the Númenóreans who survived the fall of their island kingdom (Númenor) and came to Eriador in Middle-earth, led at first by Elendil and his sons. 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 in Evendim. The surviving Dúnedain population of Arnor retreated to the Angle south of Rivendell. In the meantime the southern Dúnedain intermarried more and more with so-called Middle Men, except in some regions (such as Dol Amroth).
During and even before the War of the Ring, Dúnedain Rangers went through a variety of different duties. Some were stationed around the Shire, protecting it from the forces of darkness. Others simply patrolled the northern lands, hunting and defeating any enemies they found. In general, Dúnedain Rangers mainly took care of themselves and of lands of the Free Peoples, though if they were called upon to battle (by Gondor or some other land in need) they were quite willing to do so.
Rangers used a variety of weapons to achieve victory in battles. Non-canonical information hints that they preferred bows and archery as their primary weapons, though this is not always the case (Aragorn, for example, used a sword). They also used swords to engage in close combat if necessary. The Dúnedain mainly rely on stealth as an advantage rather than an actual face-to-face confrontation. It is also hinted that their battle skill was greater than that of a standard Gondorian soldier or archer.
Direct descendants of the Dúnedain are known to live longer than normal Men. A good example is Aragorn who, in the movies, tells Éowyn he is 87 years old, although he appears to be relatively young. (It is said that Dunedain live three times longer than normal Men; that would translate into 240 to 250 years of average lifespan, given normal human lifespan of 80 years. It is possible with the blood of the Dúnedain renewed by Aragorn and Arwen's marriage that some generations thereafter would experience lifetimes similar to that of the generations following Elros - between 400 and 500 years of life).
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.
The People of Middle-earth