Unicorns are pointy horses. They don't have one corn though, for some reason, they have one horn. They are magical creatures. The only one we've come across was a refugee from the Land of the Faeries, the Queen's pet. It stank atrociously, and was maddened on reaching the "real" dimension of the Disc to find that time - to which it was not ordinarily subject - was passing and that the sky was only blue...and the Queen's unthinking cruelty was no longer in sole command of its head. In short, it was insane - as evidenced by its charging Granny Weatherwax - a thing no mortal creature would ever do. Animals are extremely good at knowing what would be more-than-suicidal. The unicorn was taken by Granny Weatherwax to Jason Ogg's Smithy, where she had him shoe it with silver horseshoes.
And there's one thing that everybody knows about unicorns: it takes a virgin to be able to tame them, hence the ease with which Granny does so, leading it to Jason Ogg's smithy tethered by just one of her silver hairs. A unicorn hunter was among the heroes who visited Ankh-Morpork during the attack of the dragon, but decided that the reward offered was not high enough. He was described as a quite man with a shy smile.