Well, technically speaking, the word "Alicorn" through most of time has referred to the theoretical substance that made up a unicorn's horn. In the late medieval period and in the early renaissance, "Unicorn Horns" were supposedly powerful artefacts that aided in healing and the like. Queen Elizabeth the first owned one and it was valued at being equal to 3,000 ounces of gold. It was, of course, a narwhal horn. Anyway, in the show, it’s a term used to refer to the likes of Celestia and Luna, who have both horns and wings. All Princesses in series have both wings and a horn. Is this a trend, or a coincidence? Which one implies the other? Are they royals due to their Alicorn nature, or are they only Alicorns because they belong to the royal bloodline? Prince Blueblood, it may be noted, is not an Alicorn. So it’s likely that it’s just an inherent trait. Let's break this down over-analytically: Cadence is Celestia's niece, which either means there’s a third Alicorn sibling somewhere, or Luna had children at some point. Blueblood is not an Alicorn, but part of the royal family, meaning that you don’t have to be an Alicorn to be part of the Royal family. We can state with reasonable certainty that Alicorns possess some serious magical power; after all, it would take an enormous amount of energy to move celestial bodies through the interplanetary medium [of space]. The case of Princess Cadence further strengthens this theory. We’ve seen that she can change the thoughts and feelings of ponies through magic, which, one can assume, is no easy task. If it was easy, wouldn’t everyone be doing it? Now we get onto the interesting part. Celestia, Luna and Cadence all have some sort of unique power, and they are all Alicorns. Prince Blueblood, as far as I can tell, has no unique power. Unless of course being terribly un-gentlemanly counts as a “Unique power”.
Something to think about, is it not?