In Middle-Earth, this label actually applies to two different groups of people at different points in time:

In both cases it describes groups of men, the first of which (as appears in the Silmarillion) was a group of short, dark primitives also known as swarthy men who moved into Beleriand after the battle of Darog Bragollach, some for the relatively innocuous purposes of putting the fertile lands to good use and others under the suggestion of Morgoth. One tribe of Easterlings, the sons of Bór, served loyally under Maedhros in the battle of Nirnaeth Arnoediad, while another, the sons of Ulfang, proved traitorous and resulted in the pivotal defeat of the eastern army of the Elves. This latter group recieved the terrirory of Hithlum in exchange for their treachery and alternately intermarried with and enslaved the few Edain and Elves remaining in that land, dwelling there until they were destroyed with all of Morgoth's other forces in the Great Battle.

The second, unrelated, group of Easterlings (that is, men living to the east of politically-interesting territories) inhabited the area of Rhûn and began appearing in histories around the year 490 Third Age, where they started coming into conflict with the men of Gondor, frequently over the ownership of Dagorlad, the Battle Plain, notably so in years 1899 and 1944 of the Third Age. Primitive relative to the Dùnedain of Gondor, their invasions were frequently motivated by a desire to increase their standard of living through acquisition of Gondor territory, though sometimes they were spurred from idleness by Sauron, appealing to their hatred of Gondor, and some conflicts seem simply to have been the result of relatively benign population migrations rather than out of any impulse of conquest. As we leave them in the Fourth Age, the Easterlings near Gondor are (again, benignly) conquered by Elessar.

Tribes of the latter type of Easterling include the Balchoth and the Wainriders, and though their forces as described in the Battle of the Pelennor wore beards and wielded great axes, this seems to be atypical for their people.

Here's the earlier prior write-up. The editor who removed it hadn't noticed that it yet contained information mine didn't. Eventually I'll incorporate the info more seamlessly, but if I don't take this precautionary measure now, it's lost to me forever.

Tolkien: Coming from Rhûn, the land of the east. Khamul the Easterling, one of the Nazgûl was such a person.