$file = 'electricity.txt';
open(INFO, $file);
@lines = <INFO>;
close(INFO);
$counter = 1;
foreach $line (@lines)
{
    if ($line =~ /$ARGV[0]/)
    {
        print "$counter ";
        $_ = $line;
        s/$ARGV[0]/($ARGV[0])/g;
        print $line;
        $counter++;
    }
    else
    {
        print $line;
    }
}
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If you're talking about this section of the code:

$_ = $line;
s/$ARGV[0]/($ARGV[0])/g;
print $line;
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It's because $line and $_ are two different variables. your s/// is changing $_ there, so that's what you'd need to print out if you wanted to see the change.

Note: I'd change a lot of things about your script, but starting with adding use strict and use warnings to the top. Here is a cleaned up version with strictures in place:

use strict;
use warnings;

my $string = shift;

my $file = 'electricity.txt';
open my $fh, '<', $file or die $!

my $counter = 0;
while (<$fh>) {
    if (s/\Q$string\E/($string)/g) {
        $counter++;
        print "$counter ";
    }
    print;
}

close $fh;
[download]

What do the strict and warnings commands do? And what is the purpose of my before the objects? What does it do? Also, what is the purpose of my $string = shift;? I don't understand the if (s/\Q$string\E/($string)/g) { conditional either. Thank you for all of your help

Oh, duh. Thanks. I can't believe I overlooked that.