To "open up to" someone means to tell them your personal thoughts.
I love talking to you because I feel like I can really open up to you.
"Opening up" usually means that you tell someone an emotional story or a secret about your life. English speakers think of "opening up" as a good thing. It's something that you're supposed to do in order to deal with problems in your life.
People that you can "open up to" include:
- a family member
- a friend
- a counselor