She's lonely; other than her sister, there isn't anyone there who's around her age. She feels Peter actually understands her, and she ends up enjoying spending so much time with him. Also, things in the Annex were starting to get tense with everyone, she wanted a friend and despite what Mrs. Van daan said Peter and Anne continued to "hang out". They enjoyed the peace.
Hope this helps, feel free to copy/paste, I don't care. :)
