Derogatory term in the Brony community used to refer to the controversial alicorn princess version of the My Little Pony character Twilight Sparkle. Alicorns are demigod-like beings in the poniverse that have both wings and a unicorn's horn, and when the show's producers decided to transform one of the show's main unicorn characters into an Alicorn Princess, a large section of the fandom did not receive it well.
Twonicorns are mystical creatures similar to unicorns, but with two horns (hence the TWOnicorn bit). They are, however, entirely their own species. Twonicorns are quite shy by nature and are so few that many people do not believe in their existence. This may also be due to the fact that that they reside in the countryside in carefully kept holes in the ground, out of the sight of prying human eyes. These holes are where they hoard any sparkly items they find and host the most magnificent tea parties.
A manicorn that is still growing up, thus called a teenicorn. Prime examples of teenicorns are characters portrayed by Michael Cera. Other such examples are Keith (Eric Stoltz) from "Some Kind of Wonderful", Jake Ryan (Michael Schoeffling) from "Sixteen Candles", and Chris (River Phoenix) from "Stand By Me".