The Rohirrim, sometimes called the Horse-lords, were Humans that settled in the land of Rohan, named after them. The name Rohirrim was mostly used by outsiders: the name they had for themselves was Eorlingas, after their king Eorl the Young who had first brought them to Rohan. The terms Riders of Rohan and Riders of the Mark are commonly used and refer specifically to their mounted soldiers. The King's Riders were specifically the Riders who formed the bodyguard of the King.
The Rohirrim Humans were descendants of the Edain of the First Age. They did not go to Beleriand like the Edain who were later rewarded with the island of Númenor by the Valar. The ancestors of the Rohirrim were known as the Éothéod.