The most popular conception of fairies is that of tiny people with wings, but not all fairy lore uses this idea. In fact, it appears to be a relatively recent development, with the more traditional take of fairies making them more like minor deities. They play such roles in many fairy tales, and L. Frank Baum adopted this general idea in his own books. Well, most of the time, anyway. His definition of the word "fairy" seems to vary considerably, sometimes even within the same volume. As I mentioned in this post, The Life and Adventures of Santa Claus makes Fairies specifically the guardians of mankind, but it's used elsewhere in Baum's work to refer to any and all immortal beings. Sometimes it's used even more broadly than that, which I think reflected popular usage at the time. Even today, the category we call "fairy tales" includes a great many works (perhaps the majority, in fact) that don't include fairies at all. Similarly, "fairyland" often just means "magical land," not specifically a place where actual fairies live. I believe the first reference to the Land of Oz as a fairyland or fairy country appears in Ozma of Oz, but he must have had it in mind before, as one of the proposed titles for the original The Wonderful Wizard of Oz was From Kansas to Fairyland. The name seems to primarily separate such lands from non-magical civilized countries like our own. In Emerald City, Baum writes, "Oz being a fairy country, the people were, of course, fairy people; but that does not mean that all of them were very unlike the people of our own world." And in Road, Dorothy refers to the Tin Woodman as "a fairy prince." Baum was obviously not above using the term loosely, as the Tin Woodman is certainly not an immortal with magic powers. Ozma is eventually revealed to be a full-fledged fairy, but we don't actually see hints of this until Emerald City, and she doesn't display any real magic powers until Lost Princess. Tin Woodman tells us that Oz was enchanted by a fairy queen named Lurline, but this happens so late in Baum's books that it seems to be almost an afterthought on his part, although later authors did more with this.
One interesting character to examine in this light is Glinda, who largely plays the role of the fairy godmother, but is not a fairy herself. Or is she? In Lost Princess, the Wizard of Oz says, "Ozma is a fairy, and so is Glinda, so no power can kill or destroy them, but you girls are all mortals and so are Button-Bright and I, so we must watch out for ourselves." And in Jack Snow's Shaggy Man, the King of the Fairy Beavers insists, "Glinda is a fairy just as Ozma is." He goes on to say that "fairies...are creatures of the light and air," even though this is hardly always the case. The Nomes, for instance, are considered rock fairies, and they live underground. Anyway, despite these statements, I think most of the evidence points to Glinda being a human who has achieved a lot of magical power, rather than a magical being in and of herself. That said, it's certainly not impossible that she has some fairy blood.