The barbed wire tattoo is gotten for 3 reasons only:
1) Coolness / fit in. Others have the barbed wire on their arm or leg or wherever, and thus it looks cool. It allows you to circle your arm or leg with a pattern, like a tribal marking.
2) Trying to say you're tough/badass/hardcore/insane. Movies have been done with villans wearing barbed wire or razor wire as part of their ensemble, giving a visual reference to just "how tough" they are. They like to be able to flex their arm or leg to make the tattoo look bigger or look like the arm is pressing against the wire. The blood or painful looking parts of it are the person's way of saying they think they're tough and probably could stand REAL barbed wire wrapped up against their skin.
3) It's cheap/easy/convenient to get that kind of tattoo. It's not a complicated pattern. There's not a lot of color. Someone could do it in a heartbeat. If you don't know any better, or don't care, a barbed wire tattoo is just as good as a real piece of body art.