if ($volume =~ $vol_to_parse) {
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    if ($volume =~ /$vol_to_parse/) {
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since it's a regular expression.

Update:  Thanks to AnomalousMonk below for pointing out that my "fix" above was incorrect, and for teaching me something new!

A couple of other suggestions, though:

You should get in the habit of using warnings (in addition to strict).

Note that you've got a lot of string concatenation which is unnecessary, due to the interpolation nature of quotation marks ("double quotes").  In general, everywhere you've got a <close-quotes> <dot> <open-quotes> combination, you can remove it without change to your functionality (but it's much easier to read!)

For example, you can change:

print "Using: "."vol: $vol_to_parse". " and " . "file: $file_to_parse"
+ . "\n";
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to:

print "Using: vol: $vol_to_parse and file: $file_to_parse\n";
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Finally, if you use $! after system calls like open, it will tell you the exact error you got (eg. "file not found", "permission error", etc.):

    open(DAT, "<", $file_to_parse) || die "Could not open file! ($!)\n
+";
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There are numerous other issues that I'll address by example rather than explanation.  Here's a stripped-down, cleaned-up and working version of your program:

#!/usr/bin/perl

# Libraries
use strict;
use warnings;
use Getopt::Long;

# Globals and default arguments
my $vol_to_parse  = "john";
my $file_to_parse = "file1.txt";
my @raw_data;

# Main program
process_args();
open_sesame();
pars0r();

# Subroutines
sub process_args {
    GetOptions (
        'v=s' => \$vol_to_parse,
        'h=s' => \$file_to_parse,
    ) or die "syntax:  $0  -v <volume> -h <file>\n";
}

sub open_sesame{
    open(DAT, "<", $file_to_parse) || die "Could not open file! ($!)\n
+";
    chomp(@raw_data = <DAT>);
    close(DAT);     
}

sub pars0r{  
    foreach my $volume (@raw_data) {
        if ($volume =~ /$vol_to_parse/) {
            print "$vol_to_parse got got \n"; 
        }
    }
}
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Feel free to ask other questions (of course), and keep up the good Perl learning!