This article is from the Backgammon FAQ, by Mark Damish firstname.lastname@example.org with numerous contributions by others.
In money play, if player A doubles, and player B believes that he is a
favorite holding the cube, he may turn the cube an extra notch as he
takes, and keep the cube on his own side. For example, if A makes an
initial double to 2, B may, instead of taking the double and holding a
2 cube, say ``beaver'', turn the cube an extra notch to 4, and
continue the game holding a 4 cube.
If A believes that B's beaver was in error, some play that he may then
``raccoon'', turning the cube yet another notch (to 8 in the example).
Cube ownership remains with B. B may then if he wishes turn the cube
yet another notch, saying ``aardvark'', or ``otter'' or whatever silly
animal name he prefers (the correct animal is a matter of
controversy), and so forth.
Beavers and the rest of the animals may be played or not in money
play, as the players wish.
Beavers and other animals are never used in match play.
-- Andy Latto
It should be noted that the original cube turner can drop a beaver.
For example, suppose I miscount a bearoff and double, you accept and
say you want to beaver. I realize something is wrong and recount. If I
am horribly behind, I can drop the beaver, paying you the value on the
cube before you beavered.
-michael j zehr