The wolf is a huge part of being a werewolf. Not only does it allow you to shift (obviously), but it also gives the human part extraordinary senses, reflexes, strength, and speed. In most books, it also allows the human to mind-link other wolves in the Pack.
When you read a werewolf book, usually, when the human shifts into the wolf, the wolf part is the color of the human's natural hair. Therefore, a lot of times, you would be able to identify the wolf to the human (and vice versa). In Bitten, this is the way the fur works.
As discussed in the previous chapter, the wolf is like the subconscious of it's human. It's usually the one who is instinctual, and often makes the human behave more or less like a wolf. It's also the one who tells the human where it went wrong, and is sometimes sarcastic about it.