Declaring class members or methods as static makes them accessible without needing an instantiation of the class. A member declared as static can not be accessed with an instantiated class object (though a static method can).
The static declaration must be after the visibility declaration. For compatibility with PHP 4, if no visibility declaration is used, then the member or method will be treated as if it was declared as public.
Because static methods are callable without an instance of the object created, the pseudo variable $this is not available inside the method declared as static.
In fact static method calls are resolved at compile time. When using an explicit class name the method is already identified completely and no inheritance rules apply. If the call is done by self then self is translated to the current class, that is the class the code belongs to. Here also no inheritance rules apply.
Static properties cannot be accessed through the object using the arrow operator ->.
Calling non-static methods statically generates an E_STRICT level warning.