They give you physical proof that whatever unlikely event you're going to talk about next has actually occurred.
See this weird mark on my arm? Well, you know when glass falls on top of people in Hollywood movies and nobody gets hurt? Complete proof that it's bullshit. I was under falling glass and had cuts so deep, I don't want to know what it was I could see in those wounds. I ended up going outside, complete covered in deep cuts and bleeding to buy a first aid kit. You should've seen the look of the guy behind the counter!
When there's nothing to talk about, you've always got stories about what happened in your life. When unsure people are actually going to believe them, you go for the stories of how you got your scars.