Mattered means that the book meant so much, it was so important to him, that he took it with him. A copy of the book means one exemplar of that specific book.

Mattered = to be of importance “Mattered so much to him…” (meaning that it meant so much, it was of great importance, there was a deeper connection) “Took a copy of it…” (a copy of an object is just a duplicate, the same thing)