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The White Horse, on a field of green, was the emblem of the land of Rohan and its Kings. It was emblazoned on many of the arms of the Rohirrim, as shown, for example, by the shield given to Merry Brandybuck by Éowyn, which bore the mark of the horse. As the royal banner of Rohan, it was borne to many battles. Théoden rode under it to the Battle of the Pelennor Fields, and it was flown by Éomer before the Gates of Mordor itself. Even after the War of the Ring, the White Horse did not rest, and we're told that it was carried into battle by Éomer in the southern lands long after the great War ended.
The White Horse is a recurring motif in mythology and prehistoric English culture. See leucippotomy.