For one thing, you are ignoring the first element of the array ( Perl arrays are zero-based ), and comparing phantom elements at the end of the array. For example, if you have this array:

@stuff = ( 90, 5, 4 );
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Your code will start with the second element, and compare the last element to a nonexistent ( and therefore undefined ) value ( $stuff[3] ).
For another thing, you are resetting the value of $highest every time a following element has a lower value. With the code as it now exists, $highest will always be the last element in the array. I urge you to work this out by hand with the short example.
Here is something that does what you want:

my $highest = 0;
foreach my $element ( @numbers ) {
   $highest = $element if $element > $highest;
}
print $highest;
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