In English-speaking countries during the 1800s and early 1900s there was some serious belief in fairies, just as there was in spirits or ghosts. They were often depicted as to be small, translucent, luminous, supernatural, somewhat mischievous, winged and capable of flight, and female. The word comes from an adjective meaning "magic" or "enchanted." At one point, people published what were said to be photographs of fairies, later acknowledged to be hoaxes.
Various mysterious but natural phenomena are sometimes said to be the work of fairies; for example, mushrooms sometimes grow in circular arrangements called "fairy rings."
James M. Barrie's 1904 play (and later book) "Peter Pan," included a fairy named Tinker Bell. "Peter Pan" was fabulously successful and has become a cultural universal in English-speaking countries, and has probably shaped the modern idea of fairies--particularly the depiction of Tinker Bell in Disney's animated cartoons.
Serious belief in fairies was already declining when Barrie wrote "Peter Pan." A character in the play says "children know such a lot now, they soon don't believe in fairies, and every time a child says, 'I don't believe in fairies,' there is a fairy somewhere that falls down dead." When Tinker Bell is dying, Peter Pan appeals to the audience to clap their hands if they believe in fairies. Under the spell of the play, children are induced to clap and some of them will say they believe in fairies, but in the US there's no serious belief in them, any more than there is in Zeus or Thor.
At some point, certainly by the 1950s but probably much earlier, the word "fairy" became slang for a male homosexual. This creates some awkwardness in discussing them.