my @b = grep EXPR, @a;
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is equivalent to

my @b;
foreach (@a) {
   if (EXPR) {
      push @b, $_;
   }
}
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In this case:

my @uniqueIPs;
foreach (@uniqueIPs) {
   if (!$counts{$_}++) {
      push @ipAddresses, $_;
   }
}
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As for post-incrementing,

$x++
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is equivalent to

my $orig_x = $x;
++$x;
$orig_x
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In this case:

my @uniqueIPs;
foreach (@uniqueIPs) {
   my $old_count = $counts{$_};
   $counts{$_}++;             # Add one to count.
   if (!$old_count) {         # If it's the first time we've seen it,
      push @ipAddresses, $_;  #    save it
   }
}
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So,

my %counts;
my @uniqueIPs = grep !$counts{$_}++, @ipAddresses;
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is short for

my @uniqueIPs;
foreach (@uniqueIPs) {
   $counts{$_}++;             # Add one to count.
   if ($counts{$_} == 1) {    # If it's the first time we've seen it,
      push @ipAddresses, $_;  #    save it
   }
}
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It is dense, but it's tried and true. Just add a comment for the less learned readers.

# Remove duplicates IP addresses by counting
# the number of times each address occurs.
my %counts;
my @uniqueIPs = grep !$counts{$_}++, @ipAddresses;
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Oh by the way, you could also write it as follows if it's less confusing:

# Remove duplicates IP addresses by counting
# the number of times each address occurs.
my %counts;
my @uniqueIPs = grep ++$counts{$_} == 1, @ipAddresses;
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Brilliant. I think if I had all of Perl explained to me this way I'd be a saint in no time.

Besides the overall deconstruction, rehearsing the pre/post incrementing has been helpful.

Thanks NetWallah and ikegami!

—Brad
"The important work of moving the world forward does not wait to be done by perfect men." George Eliot

Your welcome. In my case, it's "By explaining Perl this way, I became a saint in no time." :)

Why would the value of that first key get incremented?

my @uniqueIPs; #Just declare it as an empty array;

#  The resulting value in %count is equivalent  to the  execution of t
+his statement:
$counts{$_}++  for @ipAddresses;  # This is  the important piece.

# The hash %counts uses each ipAddress  as a key.
# The first time an IP address is encountered, the key-value pair is c
+reated, with a value of zero.
# the(++) increments that to 1.
# The next time  that IP is encountered, the value is incremented. So,
+ at the end, the value for each  key
# contains the count of occurrances for that IP address (key).

... grep !$counts{$_}++, @ipAddresses
# The "grep:searches  through  each value ($counts{$_} is the VALUE), 
+and the negation  (!)
# looks for non-zero values.  Because the operator used is post-increm
+ent($blah++), before negation,
#  the value returnedwill be zero  for First-seen  IP addresses only. 
+For second and subsequent
#  sightings of the IP,  the pre-negation value will  be non-zero,  an
+d  post-negation  will be zero.
#  "grep" filters out,  leaving only non-zero values, effectively retu
+rning all  the KEYS of %counts, which  is
#  all the unique IP's.
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