A hatstand was a device used to store hats and coats. They hung from prongs upon the stand.
The TARDIS hatstand Edit
The Doctor owned a hatstand and kept it in the console room of his TARDIS. The Fifth Doctor moved it out as he decided it no longer needed to have pride of place as he only wore a hat when he went out. The Doctor claimed to have another hatstand within the TARDIS and declared that he was to put them together so that he had a pair.
After the TARDIS was supposedly destroyed, the hatstand was all that was left. Turlough used it to threaten the colonists of Frontios, and they took it to be a device that called down meteorite storms. The Doctor and Turlough used this to their advantage, threatening the colonists into opening the research centre for them. The Doctor left the hatstand to the colonists as a gift upon his departure. (TV: Frontios)