To read and work with this book's contents, it is expected that you are already a PHP developer with a basic understanding of JavaScript, and experience of HTML and CSS.
The book will not cover jQuery in depth—there are other books available that are dedicated to it. This book is designed to help a PHP developer write some immediately-useful client-side applications without needing weeks of study.
You need to understand how CSS selectors work. A CSS selector is the part of CSS that goes to the left of the { character. jQuery selects elements by using CSS selectors, and it's an extremely powerful way of choosing the elements that you wish to work on.
HTML is a must-have for every web developer. I think we can safely say that your HTML skills are not lacking, especially because that's the environment that PHP is usually working in.
Your PHP is expected to be good. You don't need to know everything about PHP, but it is beneficial if you have already written a few full PHP projects yourself and are comfortable with reading code and quickly understanding what it does.
You are not expected to be a good JavaScript writer. It will be useful, but the book is written such that beginners should not have a problem understanding how it all fits together. As a PHP developer, you will find that JavaScript is similar to PHP anyway, so you should not have a problem reading the examples and understanding them.