Short answers, pulled from the story.
Fan service in anime and manga refers to material added to a work to please the audience rather than to serve the plot or character development. Classically it is sexual in nature, including revealing outfits, nudity, shower scenes, and poses, though it also covers meta-references and other elements aimed at dedicated fans.
The term fan service originated in Japanese, within the anime and manga fandom. Its use in manga began gaining notable momentum in the 1970s with series such as Cutie Honey, and by the 1980s elements like full frontal nudity and shower scenes had become standard in the genre.
The Gainax bounce is the animated effect of jiggling breasts, considered a form of fan service. It originated in the opening scene of Daicon IV and was subsequently adopted by other animators, including the creators of the hentai series Cream Lemon.
Princess Leia's metal bikini in the 1983 film Return of the Jedi is a widely cited example of Western fan service. Carrie Fisher's character was depicted in a revealing outfit while enslaved to the gangster Jabba the Hutt, an element critics described as an attempt to feminise the character and appeal to boys' fantasies.
Fan service for women in shoujo manga typically features male characters shown half-naked in enticing poses, and male homoeroticism such as accidental kisses is common. Robin Brenner notes that fan service aimed at women is rare in US comics culture, while in Japan series can become known specifically for this type of content.
Fan service was frequently edited out of anime and manga translated for US audiences due to differences in cultural values between Japan and the United States, as explained by Mike Tatsugawa. Western markets also had obscenity laws and rating systems, including the Comics Code Authority and the MPAA rating system, that restricted displays of nudity. Removals sometimes provoked fan backlash, as with Tenjo Tenge.