Translation:I am responsible for the book section.
"Sezione del libro," with book being similar, would translate to "section of the book" or "the book's section" and I can't imagine that would be a common phrase. You couldn't translate it as "book section," because to have a section for books requires the presence of more than one book. The weird grammar stuff going on is due to English, not Italian, and the way we tend to use nouns as adjectives.
I saw an almost identical sentence earlier in this lesson, but it said "Sono IL responsabile...". Is it correct both with and without the 'il'? The word 'il' threw me off. I thought it meant "I am the responsibility of..." , but the given correct translation for that one (with the 'il') was exactly the same as this one (without the 'il'). Does "Sono il responsabile" mean "I am the one responsible", while "Sono responsabile" means "I am responsible" maybe?