You exist "inside" your head. In English, you can say that you have "gotten in someone's head" if you understand them very well. If you do not understand someone, but you want to understand them, then you are "looking for a way in". If someone refuses to communicate their feelings with you, then they are "closed off" to you, with "no way in".
With this passage, the writer wonders if there is a way to understand another person completely. In the last sentence, the author believes that "there is a way in", meaning that there is a way to understand other people completely.