The 'dust jacket', often just referred to as the 'jacket' is a separate cover that is folded around the outside of the book. Because of this, some industry types have taken to calling the outside cover of a book 'the jacket'. (Others insist this only applies to dust jackets and not the actual covers.) So, in this case it's about printing something on either the dust jacket or cover of a book.

Oh, yes, it's also called a dust jacket, right? It hadn't crossed my mind until you mentioned it. :) Thank you very much!

Here, the author of the book is referring to a remark that a woman made about the book. She described the book as "Fifty Shades of Gray for teens". The "jacket" of a book is the outer cover. Often, a description of the book and some comments people have made about the book are printed on the cover. When the author says he wants to "put that on the jacket" he means that he wants to put the woman's comment on the cover of the book (probably alongside the description and some other comments).