The fortress where the Rohirrim make their last stand at Helm's Deep is the Hornburg.
Helm's Deep is the name of the fortified valley in the White Mountains, while the Hornburg is the castle standing at the valley's head. During the Battle of Helm's Deep on 3–4 March 3019 of the Third Age, King Théoden and Rohan's defenders retreat behind its walls as Saruman's army attacks.
The Uruk-hai eventually breach the Deeping Wall using an explosive device, but the defenders hold the Hornburg until dawn. Théoden and Aragorn then ride out, while Gandalf arrives with reinforcements led by Erkenbrand. The appearance of the Huorns from Fangorn helps complete Saruman's army's defeat.
A common mix-up is treating “Helm's Deep” and “the Hornburg” as interchangeable names. Helm's Deep is the entire defensive area and gorge; the Hornburg is its principal fortress. The name Helm's Deep comes from Helm Hammerhand, an earlier king of Rohan.