I believe its called rapport.. just through normal conversation and life stories you talk about portray that you are a normal person with similar beliefs/values and she can feel comfortable knowing that you aren't a weirdo.
Stories do a lot, and when you can manage to convey humour, high value, healthy instincts (protector of loved ones, always there for your friends), and even vulnerabilities (childhood stories of being afraid of the dark or losing your goldfish) , she will see that you are a genuine person and will feel very connected/comfortable with you. Make sure you aren't bragging about it, they are just elements and parts of the story.