The Sindarin word Edain, singular Adan (Quenya Atani, Atan) literally meant Second People, and originally referred to all Men, but later it only applied to the Men of Beleriand and their descendants.
They were divided in three large houses, or tribes:
The Bëorians were nearly wiped out by Morgoth, and the remainder of its people merged with the Hadorians to become the Númenoreans. It would seem the Haladin were completely wiped out, or at least disappeared as a seperate people.
When the Númenoreans returned to Middle-earth in the Second Age, they encountered many Men which were obviously related to the Atani: they classified these Men as Middle Men, and established friendly relations with them. Examples are the Rohirrim, the Men of Dale, and the Breelanders.
Other Men, such as the Dunlendings, were not recognised as Middle Men because they were related to the Haladin rather than Bëorians or Marachians, and they were hostile to Númenor.
A fourth kind of Men came with the Second House, and called themselves Drûg. This name was adopted in Sindarin as Drúedain: Drûg+Edain. They were a strange people, living with the Haladin in the forest of Brethil, but apparently none of them made it to Númenor. In the Third Age, their far kin were known as the Woses of Drúadan Forest.
In Celtic mythology, Edain an alternate name for Epona.