A Brazen Head is, as the name implies, a life-size model of a human head cast in brass or bronze, and often set with precious stones and with the head-dress of a priest, which is reputed to be able to answer any question.
It is said to speak in a voice like the piping of flutes, although some authorities say that it does not literally speak, but gives its answers on a scroll which issues from its mouth. Some say that it can only answer 'yes' or 'no', and that it takes questions in a frustratingly literal way. Others say that anything which a Brazen Head sees or hears, it is as if all Brazen Heads in the world have seen or heard it.
There are cryptic references in the Lesser Key of King Ranjit to 'false Heads'. But whether they give false or random answers, or cannot answer at all, is unclear.
(thanks to Telecanter for the original inspiration for this)