Unicorns are beautiful pure white horses with horns. Muggles love them, and for good reason. They're awesome.
A unicorn's horn, blood, and hair are all super magical.
They generally stay away from humans, but are more likely to come by a witch or wizard. Unicorns are no dummies.
(Harry Potter book shout out: In Harry Potter and the Sorcerer's Stone, Professor Quirrell has to kill at least two unicorns to try to keep that Voldemort growth going on the back of his head. Needless to say, killing a unicorn is bad. Very, very bad.)