The difference is that passing an array to a subroutine passes a copy of that array whereas a reference to an array you can dereference and get the actual array. Perhaps an example will help

#! perl -w
use strict;

my @array = ("0","1","2","3");
my $aref = \@array;

print "Original array: ", @array, "\n";

print "Pass original array to testnonref(): ";
testnonref(@array);
print @array, "\n";

print "Running sub passing array reference and printing array:";
testref($aref);
print @array, "\n";


sub testnonref {
        my @subarray = shift;
        $subarray[0] = "4";
}
sub testref {
        my $one = shift;
        $$one[0] = "4";
}
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Here I used your array and array reference (hases work the same way) and first I print out what the array looks like. Then I print out what the array looks like after passing it to the testnonref subroutine. Then I print out what it looks like after passing by reference. Hopefully the output will make it a little clearer:

Original array: 0123
Pass original array to testnonref(): 0123
Running sub passing array reference and printing array:4123

As you can see, passing by reference actually changes the value of your original array whereas just passing the array makes a copymakes a reference to your array using @_ and any changes are lost after the subroutine exits.

Update: thanks, I always assumed (incorrectly) that perl copied the array like other languages. This is why I love perlmonks... always learning better ways of doing things.