What does it mean when a girl says she feels safe with me?

Anonymous
I've known this girl for 2 years and recently we have come quite close with each other. She has said things to me like

1) I feel I don't have to worry around you, like I feel safe with you.
2) I'm a great guy
3) I'm scared I'm going to lose you
4) She says she can trust me
5) aww no lovely why don't you feel well
6) She kept saying she is cold, so she stands very close to me and I get her a cuddle to warm up; she didn't move away.

This behaviour she never used to be like this with me, I know that I'm the only guy she seems to be like this with.
She also sends me texts everyday, she wants to go to the movies with me. Her and I have spent time together.
What does it mean when a girl says she feels safe with me?
4 Opinion