In the 1930's someone came up with a great idea to make money backgammon more exciting: the doubling cube. Not only did it make the money game more exciting, but it was a great addition to tournament play as well.
In fact, the doubling cube makes the game so much more interesting and exciting, I, and many of my friends, have used the doubling cube idea for other games and competition. Try using the doubling cube when you are competing at golf, gin rummy, tennis, and just about any other sport or game. I've done it, and it's fun.
There are people out there who just can't get too much excitement, and I am sure that one of those people came up with the ideas of the Beaver and the Raccoon.
In money games, if someone doubles you, and you think it is a bad double and you are actually favored to win the game, you are allowed to immediately redouble but hold on to the cube. This is called a Beaver. In other words, let's say someone gives you the cube at 2 and you think you are actually favored, you can immediately turn it to 4 and still hold the cube, so that you have the ability to turn it back to 8 the next time it's your turn, or at a later time if you prefer.
But someone didn't find this to be exciting enough, and they invented the Raccoon. Let's say that you give someone the cube at 2, and they Beaver, keep the cube and turn it to 4. And let's say that you think they are wrong to do this, that you are actually a big favorite and they have made a mistake. You can then Raccoon, which means they still keep the cube, but it goes to 8.
Here's a good example. In the position below, Black is on roll and holds a 2 cube and he doubles. He should double, because he is a huge favorite to win. In fact, according to Snowie, he will win 93% of the time. Let's say that White is either a big gambler who likes to take big chances, or he is foolish and thinks he is actually favored to win the game. And let's say that White Beavers and turns the cube to 4. If I were Black, I would immediate Raccoon.
The point is, whenever you have a significant advantage, you want to get the stakes up as high as possible. For example, if you were flipping a coin, and you know the odds are 50/50, you might be willing to bet $1 on who wins. But let's say that someone says they will flip a coin 2 times, and if you get it right only one of the two times you will win. How much would you be willing to bet then? The odds are greatly in your favor... assume you call heads both times, the odds are you will win 2/3 of the time. So you might be willing to bet $10 on that one. But let's say he will flip it 3 times and you only have to get it right once... then you might be willing to bet $100.
The same thing applies to money backgammon. You start out playing for a given amount of money, but when the odds are sufficiently stacked in your favor, you should be more than willing to increase the stakes, and that is why you double.
You should ALWAYS Beaver if you are a favorite holding the cube, and you should always Raccoon if you are incorrectly Beavered AND the situation is not such that his holding the cube gives him a major advantage.
Please note. In many chouettes, Raccoons are specifically banned, simply because people don't want the stakes to get so high and so out of hand in a single game that it could hurt someone who makes a mistake. Some chouettes even ban Beavers for the same reason. And in tournament play, Beavers are not allowed.
Also note, as my good friend, Roland Dieter pointed out, that there is a level above the Raccoon, called Aardvark. If someone Raccoon's, the person who Beavered can turn the cube even once more, and that is called the Aardvark.