Comments posted to date are on target. It might help to conceptually break apart what you're doing when you mash together things like \@ or $$ or @$. Here's your example, using {} to break things up conceptually/visually:

#!/usr/bin/perl
use strict;

my @array = ('1','2','3','blue','red');

# Get an array reference (via "\@") for the array called "array"
my $array_reference = \@{array}; 

&print_array($array_reference);

# print 'blue'
# lookup the fourth array element "${X}[3]" of the X defined by $array
+_reference
print "COLOR: ${$array_reference}[3]\n";

sub print_array {
    my $reference = shift;
        # access as an array the thing defined by $reference
    foreach (@{$reference}) { print "IN THE SUB: $_\n"; }
}
[download]

The $$x and @$x are shortcuts to ${$x} and @{$x} -- in short, they tell perl how you want the reference to be interpreted -- either as a scalar or an array. The funny one might seem to be $$x[], but just as you access an element of @a with $a[], the array you could get via @{$x} you can access an element of with ${$x}[].

The tutorials suggested above are a good start for more detail

-xdg

Edited to fix display of [].