The second complicated operator is known as the scope resolution operator, and is :: - two colons next to each other. It is used in object-oriented programming when you want to be specific about what kind of function you are calling. For example, if you have a function sayhello() as well as a sayhello() function of a Person object, you would use Person::sayhello() - you resolve which sayhello() you mean by using the class name and the scope resolution operator.
The most common use for scope resolution is with the pseudo-class "parent". For example, if you want a child object to call its parent's __construct() function, you would use parent::__construct().
Scope resolution is complicated, and not used all that often, however it is important you know about it. Furthermore, there's no need to understand it fully at this point - it is explained in full in the Objects chapter.
Author's Note: Bit of trivia for you here. Internally to PHP, the scope resolution operator is called "paamayim nekudotayim", which is Hebrew for "double colon".