I suspect you are having trouble coming to grips with recursion. Recursion happens when a sub calls itself (either directly or indirectly). It is a powerful and elegant way of solving problems and works by "remembering" some state information on the subroutine call stack.

You will notice that the hanoi sub calls itself in two places - that's where the recursion happens. Notice that each time hanoi calls itself it does so with the first parameter set to one less that the value on entry thus the recursion eventually stops with $n ==1.

The following version that in essence dumps the call stack on each entry to hanoi and reports each exit from the sub may make it a little clearer (the entry numbers are the lines that hanoi was called from):

#!/usr/bin/perl -w
use strict;
use warnings;

my %piles = (A => [reverse 1..3], B => [], C => []);

dumpPiles ();
hanoi (scalar @{$piles{A}}, keys %piles);

sub hanoi {
   my ($n, $start, $end, $extra) = @_;
   
   dumpStack ();
   
   if ($n == 1) {
        report ($start, $end);
   } else {
        hanoi($n-1, $start, $extra, $end);
        report ($start, $end);
        hanoi($n-1, $extra, $end, $start);
   }
   
   print "Exiting<\n";
}

sub report {
    my ($start, $end) = @_;
    my $disk = pop @{$piles{$start}};

    print "Moved disk $disk from $start to $end.\n";
    push @{$piles{$end}}, $disk;
    dumpPiles ();
}

sub dumpPiles {
    for my $pile (sort keys %piles) {
        print "$pile: @{$piles{$pile}}\n";
    }
    print "\n";
}

sub dumpStack {
    my $index = 1; # Don't care where dumpStack was called so start at
+ 1
    my @stack;
    
    while ((my @params) = caller $index++) {
        unshift @stack, $params[2];
    }
    
    print "Entered> @stack\n";
}
[download]

Prints:

A: 3 2 1
B: 
C: 

Entered> 8
Entered> 8 18
Entered> 8 18 18
Moved disk 1 from A to C.
A: 3 2
B: 
C: 1

Exiting<
Moved disk 2 from A to B.
A: 3
B: 2
C: 1

Entered> 8 18 20
Moved disk 1 from C to B.
A: 3
B: 2 1
C: 

Exiting<
Exiting<
Moved disk 3 from A to C.
A: 
B: 2 1
C: 3

Entered> 8 20
Entered> 8 20 18
Moved disk 1 from B to A.
A: 1
B: 2
C: 3

Exiting<
Moved disk 2 from B to C.
A: 1
B: 
C: 3 2

Entered> 8 20 20
Moved disk 1 from A to C.
A: 
B: 
C: 3 2 1

Exiting<
Exiting<
Exiting<
[download]