A few more print()'s would make this clear...

Update: Fixed a typo, plus here's a modified version that makes it clearer what's happening (to me, anyhow):

#!perl -l

use strict;
use warnings;

my $some_word = 'race';

my @letters = split //, $some_word;

my (@array1, @array2);

for (1 .. @letters) {
    my @new = @letters;
    push (@array1, \@new);
    push (@array2, \@letters);
    my $myshift = shift @letters;
    push(@letters, $myshift);
    print "$_ : @letters : $array1[-1] : $array2[-1]"
}

print '';
print "array1 contains:";

foreach my $aref (@array1) {
   print "$aref => @$aref";
}

print '';
print "array2 contains:";

foreach my $aref (@array2) {
   print "$aref => @$aref";
}

__END__

1 : a c e r : ARRAY(0x8067740) : ARRAY(0x805f380)
2 : c e r a : ARRAY(0x807c91c) : ARRAY(0x805f380)
3 : e r a c : ARRAY(0x807c8c8) : ARRAY(0x805f380)
4 : r a c e : ARRAY(0x807c820) : ARRAY(0x805f380)

array1 contains:
ARRAY(0x8067740) => r a c e
ARRAY(0x807c91c) => a c e r
ARRAY(0x807c8c8) => c e r a
ARRAY(0x807c820) => e r a c

array2 contains:
ARRAY(0x805f380) => r a c e
ARRAY(0x805f380) => r a c e
ARRAY(0x805f380) => r a c e
ARRAY(0x805f380) => r a c e
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Update 2: kiat asks: (W)hy doesn't \@letters point to the changed @letters inside the loop? That's just it--it does!