It's a good way to divide the story content. This usually ends up being gratuitous shots of female anime characters. I suppose there can be fan service for females, I'd say a lot of the second half of Shoujo Kakumei Utena had female fan service. This word is usually used for younger girls. In Japan 'manga' can sometimes refer to anime too, but for the most part it's comics.
Japan is a huge place for comics.
Everyone reads them, so they publish stuff marketed to everyone from 1st grade girls to working businessmen. It's like a short comedy skit at the end of an anime. Examples of series with Omake would be Blue Seed, Video Girl Ai, and the Fushigi Yuugi OVAs. OP Opening Song, the opening song for an anime. OST Original Soundtrack.