I understand that this "refers" to the current object but it is not the actual object. How exactly does $this refer to the object. Is $this a pointer to the object?
$this is a reference. From the PHP manual:
References in PHP are a means to access the same variable content by different names. They are not like C pointers; for instance, you cannot perform pointer arithmetic using them, they are not actual memory addresses, and so on. See What References Are Not for more information. Instead, they are symbol table aliases. Note that in PHP, variable name and variable content are different, so the same content can have different names. The closest analogy is with Unix filenames and files - variable names are directory entries, while variable content is the file itself. References can be likened to hardlinking in Unix filesystem.
From the manual:
The pseudo-variable $this is available when a method is called from within an object context. $this is a reference to the calling object (usually the object to which the method belongs, but possibly another object, if the method is called statically from the context of a secondary object).