I just noticed that I could use an a variable as an argument, like this: $variable = "This's a string."; function('$variable'), and not like this: function('This's a string');. I can see why I can't do the latter, but I don't understand what's happening behind the scenes that meakes the first example work.
Have you heard about formal languages? The parser keeps track of the context, and so, it knows what the expected characters are and what not.
In the moment you close the already opened string, you're going back to the context before the opening of the string (that is, in the context of a function call in this case).
The relevant php-internal pieces of codes are:
These are the relevant chucks of C code that make it work. They are part of the inner workings of PHP (particularily, the Zend Engine).
PHP does not anticipate anything, it really reads everything char by char and it issues a parsing error as soon as it finds an unexpected TOKEN in a semantic context where it's not allowed to be.
In your case, it reads the token 'This' and the scanner matches a new string. Then it goes on reading s and when it finds a space, it turns the s into a constant. As the constant and the previously found token 'This' together don't form any known reduction (the possible reductions are described in the parser-link I've given you above), the parser issues an error like
Unexpected T_STRING
As you can deduce from this message, it is really referring to what it has found (or what it hopes it has found), so there's really no anticipation of anything.
Your question itself is wrong in the sense that there's no apostroph in the variable (in the variable's identifier). You may have an apostroph in the variable's value. Do not confuse them. A value can stand alone, without a variable:
<?php
'That\'s fine';
42;
(this is a valid PHP code which just loads those values into memory)