Generally any situation or scene in a movie, cartoon, comic, or
even real life in which a scene is done specifically to cater to what the fans want to see, divorced from a plot or any other non-catering need. Often mistaken as invented by Japanese anime, the
truth of the matter is that Hollywood movies and
American TV shows in particular had been using this concept for years, if not decades, before anime ever even existed; however, the coined word itself DID start within anime fandoms to reference scenes of near-nudity that held no part to the overall plot of the episode/movie/etc.
The first
film to involve nudity in the
US was 1959, whereas the advent of the modern style and tradition of anime was in the late
60's, hence fanservice existed prior to anime.