Here's my deconstruction, split apart, unusual variables replaced, and commented:

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

my $source='Just another Perl hacker.';  # previously ($_{_})
my $reversed='';                         # previously ($_{__})
my @split_source = $source =~ /./g;      # previously (@_)

$" = $/;  # arrays assigned to strings are separated by newlines
          # only thing this does is add the final newline

while(@split_source){  # for each character in the array
    $reversed .= pop @split_source;  # concat it to the reversed strin
+g
}

my @stages = ($reversed); 

my %E;  # previously (%;)
my @F;  # previously (@;)
my $G;  # previously ($/)

# while $G isn't eq source, find two random incorrect characters
# and swap them, pushing the result onto @stages
while(($G = $stages[-1]) ne $source) {
    @E{0..24} = map{pos $source = pos $G = $_;  # start searching at $
+_
                    ($a) = $G =~/./g;           # find characters at t
+hat point
                    ($b) = $source =~ /./g;     # and compare them
                    "$a" eq $b                  # expr same as substr(
+$source,$_,1) eq substr($G,$_,1)
                    } (0..24);                  # so $E{n} is true if 
+nth letter of G is correct
    @F = grep{!$E{$_}} keys(%E);                # @F is list of incorr
+ect character positions
    $a = $F[rand @F];                           # pick random characte
+r position from f
    do { $b = $F[rand @F] } while ($b == $a);   # pick another random 
+character pos from f
    pos $G = $a;                                # start search pos for
+ $G at $a
    $| ||= 1;                                   # set autoflush,  this
+ need not be in the loop
    @F[0,1] = $G =~ /./g;                       # effect: $F[0] = subs
+tr($G,$a,1)
    pos $G = $b;                                # start search pos for
+ $G at $b
    @F[1,2] = $G =~ /./g;                       # effect: $F[1] = subs
+tr($G,$b,1)
    $G =~ s/(.{$a})./$1$F[1]/;                  # replaces a'th char o
+f $G with $F[1]
    $G =~ s/(.{$b})./$1$F[0]/x;                 # replaces b'th char o
+f $G with $F[0]
    @stages = (@stages => $G);                  # adds a new record to
+ @stages 
}

# do the print out!
for(@stages){ # for each stage
    s/^/\r/;  # add a carriage return at the beginning
    print $_; # print it
    select undef,undef,undef,0.1;  # wait .1 seconds
}

print" :-)";
sleep 1;
print "@{['','']}"; # because $" set to $/, this just prints a newline
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