A little more explanation:

use strict;
use warnings;
use CGI;
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Use strict and -w, except of course for one-liners and/or short throwaway scripts. Note that the warnings pragma only works under Perl v5.6.0+.

my $q = CGI->new;
my @names = $q->param;
my %param;
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This instantiates the CGI object and fills @names with the parameter list, then declares %param, to be used later.

foreach my $name (@names)
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Iterating over each parameter in order,

{
   $param{$name} = $q->param($name);
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Set the value in the parameter hash ($param{$name}) to the parameter value ($q->param($name))...

   print "$name: $param{$name}", $q->br;
}
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... and print it; the $name and $param{$name} values are interpolated into the string. $q->br just generates an empty BR tag.

The other version:

use strict;
use warnings;
use CGI;
my $q = CGI->new;
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Same as before.

my %params = map { $_, $q->param($_) } ($q->param);
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This simultaneously instantiates %params and fills it with, for each element in $q->param (the parameter list), the name ($_, the placeholder variable -- see map / perlvar) plus the value ($q->param($_)). When this is put into a hash these pairs turn into keys and values.

print join $q->br, map { "$_: $params{$_}" } ($q->param);
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This first takes the parameter list ($q->param) and maps each element to the string "$_: $params{$_}" which is the name ($_) plus a colon, space, and value ($params{$_}) -- accessing an element of the params hash with key being the name. Then it joins these strings together with the empty BR tag, and prints the result. Hope this helps.