Familiarity With Relevant Subject Matter
It's never a good idea to walk into any test without knowing the information from back to front. Even if you get to use your book while you're answering questions, you still have to be aware of what's going on in the test. Ideally, during open-book tests, your book should be a reference tool that you use in addition to existing knowledge and understanding, not in place of it. An open-book exam may require you to apply the material to new situations, rather than simply recalling memorized data.
If you rely on your book without preparing beforehand, some finer points in questions - or, in worse-case scenarios, entire questions - might confuse or derail you. Studying before an open-book test or quiz will help you be better prepared to quickly comprehend questions.
Knowing Where to Look
Precious time can be wasted if you don't know exactly where the information you're looking for is located. Reading over the chapters or sections that are covered on an open-book test, organizing your notes to match the information in the text, and making notes on passages that seem particularly relevant (if that's allowed, of course) will help you get correct answers more quickly. Obviously, you don't want to waste test time doing this, so a study session before the open-book test would be necessary.
Saving Time by Using Your Brain
Even if your open-book test isn't being timed, there's likely some sort of deadline for when you need to finish, even if it's a matter of days. You don't want to spend all your time working on this test. Saving time is important, and you can do that by saving yourself the hassle of leafing through your book every time you go to answer a question. Understanding the test material before you take the test might allow you to answer questions without bothering too much with the book, if at all.
Understanding the Big Picture
In some cases, your teacher or professor might intentionally put questions on an open-book test that can't be completely answered by simply looking in the book. They might ask for details mentioned in supplemental assignments or lectures. They might ask for your opinion or interpretation of a fact or issue. Studying all of your course materials, from the book to class notes and graded assignments, means being prepared to answer any kind of question that comes your way on an open-book test.
You can use your study style to prepare for any kind of test!