Unicorns are horses with horns. They are some of the rarest beasts alive in the Elven world. There are only 185 of them alive (however, there may be new born), as shown in book one when Dex Dizznee gives Sophie a Unicorn Prattles Pin. Fitz describes a baby unicorn as slimy, just after it is born.
The Heks family is especially known for generations of unicorn breeding and care.