As I said, I have made some temporary references with the first statement. In my case this is an array reference (think about it like a pointer to an array) containing the filename together with the mtime as two separate array items.
To access an item from a normal array by index you will
$array[0], $array[1]
If the corresponding array is pointed to by a reference and you need to access an item through the reference, that becomes
$$arrayref[0], $$arrayref[1]
OR (both syntax will work)
$arrayref->[0], $arrayref->[1]
which literally means "dereference and then index in the underlying array".
Understanding these require some knowledge about references in Perl.
The official page that talks about this:
http://perldoc.perl.org/perlref.html