An Éoherë is the full Muster of Rohan at any given time. It is made up of one hundred Éored - units of 120 trained riders plus their captain. A member of the Éoherë can serve a term or on a permanent basis.
During the first three hundred-plus years of Rohan's existence, the term "Éored" was used widely to describe any significant number of Riders. Under Folcwine King son of Folca, fourteenth King of the Mark, the military of Rohan was reordered. Under Folcwine, one Éored was made up of 120 riders including their captain. Each Éored was also supposed to comprise one one-hundredth of the whole Muster of Rohan, not including the household of the King.
An Éored was a group of trained warriors who rode as a unit. Under the military reorganization in the time of King Folcwine, the size of a full Éored was determined to be at least 120 men. One Éored was one hundredth of the Éoherë - the full muster of Rohan. The Riders of an Éored could serve for a term or on a permanent basis. A Captain led each Éored. In times of war or unrest, the Marshals of the Mark each had a battle-ready Éored as part of his household, which he could command at his discretion.
The changes made by Folcwine lasted through the time of the War of the Ring. While the Éoherë commanded by Théoden King son of Thengel at the Battle of the Pelennor Fields did not number much more than half of the 12,000 riders supossed to be a full muster of Rohan, it was possibly the largest riding of the Rohirrim in history. Éowyn (disguised as a Rider named Dernhelm) and Merry Brandybuck rode with the Éored commanded by Elfhelm to the Battle of the Pelennor Fields on March 15. When the Rohirrim charged onto the battlefield, Éomer led the first Éored in the center while Elfhelm's Éored was on the right flank and Grimbold's was on the left flank and the other companies followed behind. King Théoden rode before them all.
The word Éoherë comes from the Anglo-Saxon Old English (which the tongue of Rohan was modelled after); it is made up of the words eoh meaning "horse" and herë meaning "army." Likewise Éored contains the words 'eoh' and 'rád' (horse, riding or rode).