You found that the book you were going to order online is in stock at your neighborhood bookstore (it's a near fantasy for your neighborhood bookstore to stock a book you actually want, but it's just an example! It applies for any kind of shopping list).
You copy the ISBN from your desktop browser, but rather than copy it on paper, you enter it in tool X. Tool X will make that number available on your iPhone so that it's handy when you ask for help at the bookstore.
Does Apple produce such a tool X? You could use Google Keep, or you could email yourself and pick up the mail from your phone, but I'm wondering if Apple has a native application for this use-case in its eco-system.