OOP is a programming paradigm which is "a fundamental style of programming regarding how solutions to problems are to be formulated in a programming language." (from Wikipedia)

Different paradigms provide different approaches to solving problems; for example, OOP looks to thinking of a program as a collection of objects which can interact with one another. Your own analogy of seeing a program as a "society" of communicating functions (objects) is a start towards thinking in an object-oriented way.

If you really want to delve into what OOP is all about, my first suggestion will always be to forget trying to 'learn' OOP with specific regards to any individual programming language (PHP). Instead, it is important to grasp the wider, overarching principles at work without getting bogged down by language syntax. Even better, learn OOP as part of a wider understanding of the other available programming paradigms which are just as useful tools in a programmer's arsenal.