"This is named after the random musical number sung by a big-lipped alligator towards the end of the film All Dogs Go To Heaven. A scene that comes right the fuck out of nowhere, has little to no bearing whatsoever on the plot, is WAY over the top in terms of ridiculousness, even within the context of the movie; and after it happens, no one ever speaks of it again."
- The Nostalgia Chick, Internet reviewer and coiner of the term.
There are three major criteria a scene must have to be considered a Big-Lipped Alligator Moment (AKA, BLAM). It must have no foreshadowing. This scene literally came out of nowhere, and has no place in the story. It must be strange, even in context and by the narrative setting's own logic. And it must never be mentioned again.
Big-Lipped Alligator Moments are usually found in movies or TV shows in the form of indulgent, plot-less dream or musical sequences, but they can crop up in other forms of media and under other guises. When done well (or at least as well as something that literally has nothing to do with the story can be done), it can result in surrealist humor. When done poorly or as the result of bad story telling (as per the usual), this can result in the audience just wondering what the hell the creators were smoking.
Examples include: The titular singing alligator from All Dogs Go To Heaven, the dragon's song in Quest for Camelot that ends in an Elvis impersonation, Spiderman 3's weird emo dance scene, and the singing lizard from Fern Gully.
Shows like Family Guy and South Park might as well be called "Big-Lipped Alligator Moment, the Series" because of how often they rely on this joke. Gangam Style might be a very meta, real life BLAM, demonstrating that while truth isn't necessarily stranger than fiction, it certainly tries its best sometimes.
The Noistalgia Chick's page at That Guy With The Glasses.