This is possibly my single biggest mistake when number closing girls who later flaked. Being unafraid to tell a girl about yourself is going to be attractive to her. It shows you have nothing to hide and are willing to get to know her as well as letting her get to know about you. While you can go deep and tell stories from your childhood etc, this is not always necessary. You can talk about something you did that week or something related to your initial conversation. Don't feel you have to change the subject for the sake of it.

Just showing a willingness to not hide behind the facade of a 'cool' player image is enough to demonstrate your real character and begin to generate real attraction.