The Red Arrow was a way Gondor summoned its allies in time of need.
Its flights were black and its barbs were made of steel, and it took its name from a mark of red painted on the arrow's tip, standing for blood to show the situation was serious. The black flights were like the Orc arrows.
First mention of the Red Arrow is when Borondir of Gondor and five other messengers rode north along Anduin to seek out Gondor's old allies, the Éothéod, when Gondor was being overrun by Easterlings, in 2509 T.A.. Borondir was the only survivor, and presented the Red Arrow to the Éothéod King Eorl the Young.
Later it became a summons for the Rohirrim. The Red Arrow was presented to Rohan by Hirgon in the War of the Ring, and Théoden King rode out with the Muster of Rohan to the Battle of the Pelennor Fields.
It is not certain where the Red Arrow came from: it is possible that the tradition was an old one and that Gondor had always summoned its allies this way, but another possibility is that Borondir actually took an Orc arrow with a bloody tip to present to the Éothéod, to prove that the situation was as bad as his message stated.