Though there is not one correct answer to this question, certainly there is a correct approach to coming up with an answer. Rather than simply giving you my opinion, I will propose a strategy to help you come up with an answer of your own.
I think the best way to answer this question is to consider the context surrounding the writing of this little book:
- Who is Max? Who is Liesel? What is their relationship?
- What does the gesture of Max's book alone say about his character? What does it say about his feelings towards Liesel?
- What does the story of The Standover Man reveal about Max's character?
- How would you feel if you were Liesel and you received such an intimate gift?
Max alone is important to Liesel. It is clear that even before he writes this book, Liesel cares very much about him, though it isn't immediately clear why. It is also clear that Max cares very much for Liesel. For Max, a Jew in hiding, Liesel is one character who seems to bear honest and unconditional concern, as well as a childlike sense of acceptance of him, despite the world she is growing up in.
As a gift to Liesel, this book is very personal because reading is her most prized accomplishment. As a gift from Max, this book is very personal because in it, he reveals himself to her. He makes himself vulnerable. But also, he thanks her and shows her how much she means to him.
I encourage you to consider the questions above and really put some thought into your own answer to the original question. One beauty of literary discussion is that answers can be very personal even when they are textually supported.