If a
fansub is a not-for-profit subtitled
anime, then a
fandub is a not-for-profit parody
dub (that is, an
English voiceover of (usually) an anime title of some type.
Such dubs are not serious interpretations, but rather over-the-top send-ups of the original material, with voices and soundtrack provided by fans with way too much time on their hands.
Examples of classic fandubs include Fast Food Freedom Fighters, a dub of Project: A-ko ("They're from the National Institute of Mealtime Health!" "NIMH! Those rats!"), Voltron: Hell-bent for Leather ("Form arms and legs! Form-- Ah, fuck it, you know the drill"), Ranma 1/3 ("N-E-K-O? That's a weird way to spell 'cocaine'.), and many many others.
Beware, though, sometimes fandubs are funny because they're full of well-written in-jokes, but sometimes they are funny because they're absolutely obscene. Ranma 1/3 is a good example of the latter.