A term used to describe fan fictions that take previously created characters and put them as a pair. It usually refers to romantic relationships, but it can refer platonic ones as well. (Just think of "shipping" as short for "relationSHIP".)

In fanfic, putting characters into a romantic relationship, such as writing Ash + Misty from Pokemon as a couple. Often plays on perceived chemistry between characters in the original series. Abbreviated form of the word relationshipping.

Fandom uses this word as a verb to denote their interest in the possible (and perhaps more often impossible) romantic relationship between two characters in a piece of fiction belonging to any medium. It's really never used in a platonic way, but if it ever is, people tend to separately emphasize that they are using it platonically.

Usually written: Character/Character or CharacterxCharacter. Fanfiction without any shipping, or with little emphasis on ship is usually labeled genfic, which there is a depressing lack of.

Also, can be made from inanimate objects. Almost anything can be "shipped".