Thanks, Tom -- that link was perfect! Here's a brief excerpt:
"Within a class definition, you do not know under which name the object will be accessible in your program: At the time the Cart class was written, it was unknown that the object will be named $cart or $another_cart later. Thus, you cannot write $cart->items within the Cart class itself. Instead, in order to be able to access it's own functions and variables from within a class, one can use the pseudo-variable $this which can be read as 'my own' or 'current object'. Thus, '$this->items[$artnr] += $num' can be read as 'add $num to the $artnr counter of my own items array' or 'add $num to the $artnr counter of the items array within the current object'. "
