This is purely headcanon, but I theorize that they have some inborn connection to emotions. They seemingly change color and stuff based on their emotions, and the Crystal Heart is able to channel and concentrate all of their emotions.
Also, ever think of how odd and unfitting it is that given the other alicorns, there's a princess of love? Well, they say that alicorns possess the racial qualities of "all three" races, but I think Cadence, being the crystal princess... somehow, has unicorn, pegasus, and crystal pony traits instead of earth pony. This sets her apart from Celestia and Luna, giving her both her unique appearance and magic.