Faeries are obviously the mythical beings you hear about, but they are also part of the folklore all over the world. They're the fair folk, the fae, good folk, the fairies. Sometimes when people say "faerie," they refer to the otherworldy Realm of Faerie to which people are sometimes thought to be spirited away and hidden for many years, usually children. Sometimes the word "faerie" refers to an actual historical race of people who gradually disappeared, according to legend. Most often the word "faerie" is just an umbrella term for magickal, mythical, or mystical creatures who, depending on who you ask, may or may not exist.

Here is a rather large list of types of faeries.

This is obviously far from comprehensive, but if I find more I can add to this list, I shall do so in good time.