Do I have to understand object-oriented programming to become a good PHP programmer, or even to finish this book?
Not at all. In fact, the projects in this book are procedural and do not contain object-oriented programming! Object-oriented programming is an organizational approach intended to improve the reusability and extensibility of the code that makes up a given application. You might not know enough about your project in the beginning stages of development to fully plan for an object-oriented design. When it is completeor, at least, approaching a solid stateyou might start to see areas in which an object-oriented approach can be taken, and you might start to combine your code into classes, properties, and methods. But for the most part, simple scripts performing particular duties are not written in object-oriented fashion unless it is your background and comes naturally to you.
For a great deal more information on the object model in PHP 5, see the appropriate section of the PHP Manual, at http://www.php.net/manual/en/language.oop5.php.