In Middle-earth, the term Man theoretically refers to any member of the race of Men, just as "Elf" can apply to any of the Elves or "Dwarf" to any of the Dwarves. In practice, of course, things are a little different, but hey, how many humans know that a male elf is properly called an ellon and a female elf is properly called an elleth?
Divisions of Men
The Men of Middle-earth are divided into three groupings: High People, Middle People, and Wild People.
The High People are the Númenoreans and their descendants, including the Rangers of the North and the people of Gondor. They gained their distinction through association and friendship with the elves during the War of the Jewels. In Sindarin Elvish, the word for "man" is adan, plural edain, which gives rise to the term Dúnedain (Men of the West) for the Númenoreans. Although, strictly, the Elves only use the term Edain to refer to the houses of men friendly to the Elves who were the ancestors of the Númenoreans. By the time of the War of the Ring, the Rangers are their most direct descendants. In fact, one of Aragorn's many titles is "Dúnadan" (Man of the West).
The Middle People (also known as "Men of the Twilight") share much of their origins with the Edain, but they developed their cultures at a slower rate and without the direct aid of the elves. They are generally held to be relations of the Three Houses of the Edain who did not cross the Blue Mountains into Beleriand in the First Age. During the Second Age, when the Edain removed to Númenor, they chose to stay behind in Middle-earth, where they multiplied. Their most notable descendants are the Northern Men, including the Rohirrim and the Men of Dale.
The Wild People include the Easterlings and the Haradrim, the Dunlendings of the White Mountains, the Variags of Khand, and, strangest of all, the Woses or "Pukel-men" of Druwaith Iaur and the Druadan Forest on the border of Gondor and Rohan (although these were held as being part of the Edain by some Elves, hence: "Druadan"). The first three have an especially bad reputation (fighting on the side of the Big Bad and his pet wizard will do that), but on the other hand, the Woses helped the Rohirrim cross into Gondor to turn the tide at the Battle of the Pelennor Fields. Further, after the War of the Ring, it became clear that the Dunlendings were tricked by Saruman, and it is likely that the Haradrim, the Easterlings, and the Variags were threatened and lied to by Sauron. Aragorn officially pardoned them.
The Gift of Man
What all the Mannish races have in common is the Gift of Man: mortality. Unlike the elves, when Middle-earth humans die, their spirits leave the world forever and, presumably, move on to new and different things. Sure, the elves have Valinor, but who wants to kick around one place for eternity, no matter how pretty?