>I am supposed to write a function where I could pass the directory name
That sounds awfully like homework to me but I'll give you the benefit of the doubt.
Here's a solution that fits into your requirements but I would caution that japhy's solution above of using readdir is much better than your proposed solution of using backticks to run ls. Anyway, here it is.

On my system, an ls -l produces something like this. It could be different on your system!:

-rwxr-xr-x    1 rhettbull Domain U      294 Aug 31 10:59 dirs.pl
drwxr-xr-x    2 rhettbull Domain U        0 Aug 31 10:58 testdir
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It's obvious that the directory entries start with a "d" as the first character on the line. So, we parse the lines looking for a "d" at the beginning of the line. Then we parse those lines with split. Notice that I limit split to 10 columns because the directory name might have spaces in it. I call split in list context and only grab the 10th entry (the directory name) since you didn't ask for the other stuff. Note that this will miss symlinks and I caution once again to use readdir.

#!/bin/perl

use strict;
use warnings;

my $lookhere = shift || '.';

parse_dir($lookhere);

sub parse_dir
{
    my $rootdir = shift || '.';
    my @listing = `ls -l $rootdir`;
    foreach (@listing)
    {    
        chomp;
        if (/^d/)
        {
            my $dir = (split /\s+/, $_, 10)[9];
            print "$dir\n";
        }
    }
}
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Originally posted as a Categorized Answer.