Try adding a couple of print statements to your program and see what it is doing.

#! perl -slw
use strict;

my @numbers = (3, 2, 1);
my $highest;

## NOTE Perl arrays start from 0 (zero) not 1 (one).
for (my $i = 0; $i < @numbers; $i++)   {
    print "Comparing $numbers[$i] with $numbers[$i+1]";
    if ($numbers[$i] > $numbers[$i + 1])   {
        print "Setting \$highest to $numbers[$i]";
        $highest = $numbers[$i];
    }
 }

 print $highest;
__END__
[download]

prints

C:\test>217736
Comparing 3 with 2
Setting $highest to 3
Comparing 2 with 1
Setting $highest to 2
Use of uninitialized value in concatenation (.) or string at C:\test\2
+17736.pl line 8.
Comparing 1 with
Use of uninitialized value in numeric gt (>) at C:\test\217736.pl line
+ 9.
Setting $highest to 1
1
[download]

Does that make it any clearer for you?