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Its a basic trap/pitfall, you forgot to chomp or trim trailing input record separator. Its beter to trim trailing whitespace ( see trim leading & trailing whitespace )

See also

Common Perl Pitfalls / perltrap

Tutorials: Basic debugging checklist , brian's Guide to Solving Any Perl Problem

perlintro, http://learn.perl.org/books/beginning-perl/, http://perl-tutorial.org/, Tutorials: Basic debugging checklist , brian's Guide to Solving Any Perl Problem, Modern Perl book, a loose description of how experienced and effective Perl 5 programmers work....You can learn this too.

The Perl Monks Guide to the Monastery

When you input a string this way: $string1 = <STDIN>;, the string is returned with the newline ("\n"), on the end.

You either need to chomp the string to remove the newline; or add a newline to the string constant you are comparing against.

print "Enter a word: \n";
chomp($string1 = <STDIN>);
$string2 = 'Mahesh';

if($string1 eq $string2){
    print "Match \n";
    }
    else {
    print "Does not match \n";
    }
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When the user types something in response your prompt:

(which by the way would be better without the "\n"), they type in a word, and then they hit Return; and when they hit Return an invisible newline character is entered into the input stream:

So your $string1 variable will look like this:

...and that will never be eq to the string "Mahesh"

#!/usr/bin/perl -l

use autodie;
use strict qw/refs/;
use warnings FATAL => 'all';

print "Enter a word: ";

my $str1 = <STDIN>;
my $str2 = 'Mahesh';

chomp $str1;
print "Match" if $str1 eq $str2;
print "No match" unless $str1 eq $str2;
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#!/usr/bin/perl -l

use strict;
use warnings;

print "Enter a word: ";

my $str1 = <STDIN>;
my $str2 = 'Mahesh';
chomp $str1;
print $str1 eq $str2 ? 'Match' : 'No match';
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    use strict qw/refs/;
    use warnings FATAL => 'all';


Just out of curiosity: Why do you avoid enabling all strictures, but then escalate all warnings to fatality?