Maybe they think that it will make it more interesting. I think it identifies them and makes them more significant and sort of distinguishes them. Like this tatoo shows that you are part of the pack. That kind of thing.
The tattoos are to symbolize that they are part of the pack. It's not metioned in the book, but books are different than movies. Books get into the mind of the character, but movies are visual; you need a physical way to represent the pack. That's why the movie producers made the tattoo.
in old legends it is said that each pack memberhas a mark unique to their pack in thier human form. Each pack's symbol was supposedly unique and inflicted by the other pack members. It's usually a scar or burn in a certain spot or shape. Never heard one about a tattoo though..