On classic era I have a bunch of gold on horde and not so much on alliance. If I wanted to transfer that gold, mechanically I could do so by listing a piece of junk with my alliance character on the neutral auction house at a very high price, and then buy said piece of overpriced junk with my horde character.
Dottie is correct - using the neutral AH this way is in a gray zone, meaning it is legal but also that you are completely on your own here. Blizzard will not interfere if the other part does not return your gold / items / whatever.