Flavor text is text added to a playing card or a game board/piece that does not affect gameplay, but adds some context or background to the activity. This is perhaps best-known in the context of Magic: The Gathering (MtG) cards, but is found in rule books, cards, and on toy boxes.
Arguably, flavor text originated on the packaging of action figures sold in the 1980s; G.I. Joe in particular popularized having information cards giving the background of characters on the rear cardboard panel of the box, which could be cut out and saved. However, the term flavor text was apparently coined specifically for and by the MtG crowd in the 1990s, with David Howell using it around 1993, and the first written reference being in the The Magic: The Gathering Pocket Players Guide (1995), by Rich Redman.
In this context, and in most cases, flavor text specifically means short snippets of lore that is usually not referencing a larger, established narrative -- as opposed to the text accompanying action figures, which usually summarized and expanded on information already given in TV shows and comic books. These snippets are rarely more than a line or three, and in fact may be a single word or even mysterious squiggles in a lost language. They most commonly function as a caption to a piece of game art. It is traditional for flavor text to be written in italics, to indicate that it is not part of the game instructions, and has no effect on game play.
In RPGs, flavor text is often called fluff; on the internet it is often hidden in the Alt Text, and so may simply be referred to as such.