The Hornburg was a great fortress which guarded the entrance to Helms Deep. It was said by Men that:

'… in far-off days of the glory of Gondor the sea-kings built here (under the shadow of the Ered Nimrais) this fastness with the hands of giants. The Hornburg it was called, for a trumpet sounded upon the tower echoed in the Deep behind, as if armies long-forgotten were issuing to war from caves beneath the hills.'

During the War of the Ring, the Battle of the Hornburg was fought there between the Rohirrim and the army of Saruman.

The Hornburg was also, at times, referred to as the Fortress of Aglarond. The Rohirrim originally referred to the tower as the Súthburg, but after the days of Helm Hammerhand its name was changed.
Encyclopedia entry originally written by Nienna-of-the-Valar