1. A horse 2. Something trying to be more than it is. This is a popular phrase from Upright Citizen's Brigade Season 1 Episode 6 entitled: The Story of the Toad. The eager horse Harry believes that he is a magical hornless unicorn.
"I'm not a horse, I'm a hornless unicorn!"
This is when a girl, out of sheer anger, starts banging her head against a wall. Only, instead of a wall, it is another girl's vagina.
Whoah, Terrence made that girl so mad that she gave the hornless unicorn to everybody in Michigan. I wonder what he did.