What made unicorns special?
What made them special? They are mythological creatures not existing in reality. Therefore, special.
I don't think that's the question you meant to ask though. I'm in the middle of piecing together a far less trolly / jokey answer right now. In the meantime, do you want to try to re-phrase the question? Otherwise, I'll just give a history of the unicorn. Or, maybe just a read through a wikipedia article would do the trick.
One of the more interesting things about the Unicorn is how much their original lore differs from later English lore. Original lore depicted Unicorns as powerful creatures. They are even mentioned in the bible as being renowned for their physical strength, which is where theories of the term referring to the Rhinoceros originated from. They were generally depicted as something like a bull with one horn growing from the center of it's head instead of two from the sides.
It is only later in European lore that they started being depicted as horses, and that was also when we saw them attributed with the ability to sense purity and only allowing pure virgin maidens to ride or even come near them.
Then, it is later in video games and modern fiction that they started having powerful healing magic attributed to them. Although, once again with the Rhinocerous comparison, there had been some talk about unicorn horns being used in medicines before the modern fantasy lore. This is not as strong a comparison to the Rhinocerous as most would think, though. It was actually common practice in Europe to take Narwhal horns and pass them off as Unicorn horns, and then make medicine out of them.
I guess... coming back around to the original question, maybe I actually can answer it as is. Unicorns were special because, up until fairly recently, there was a lot of reason to believe they might actually be real creatures, and there were several people who very much believed it including powerful kings and queens.
This includes in cultures outside of the one the stories were born in, which actually is quite special. It is common for the native culture a mythology is passed around in to really believe the creature in question exists. It is not so common for that belief to extend to other cultures who hear about it, though. Other cultures usually dismiss their stories as superstition. It is not that way for the unicorn though.
The Greeks are the best exemplars of this. Unicorns appear NOWHERE in Greek mythology. However, a place unicorns actually DID appear in Greek text was among historical and academic writings. The Greek scholars actually believed unicorns were very much a real animal that lived in some other country, most of them stating they believed it to be a creature native to India.
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