next if $seen{ $elem }++;

"Skip to the next iteration of the loop if $seen{ $elem } is true, otherwise make $seen{ $elem } true and continue."

Check out the segment on the unary '++' operator in perlop. When the operator follows a variable, it is incremented after its evaluation. In other words, in the above code, if checks the value of $seen{ $elem } before incrementing it. Since the action "next" is taken before the increment happens, the increment is skipped. Here's longer (and probably slightly slower) equivalent code:

if ( $seen{ $elem } ) {
    next; # skip to the next loop iteration
}
else {
    $seen{ $elem } += 1;
}
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This is a common pattern that checks if you've encountered $elem before. If you have, it will not process it a second time; otherwise, it will mark $elem so that you won't process it again.

This could be used to get all the unique lines from a file, for example.

use strict;
use warnings;

open my $IN, '<', $ARGV[0]  or die("Can't read $ARGV[0]: $!");
open my $OUT, '<', $ARGV[1] or die("Can't write $ARGV[1]: $!");

my %seen;
while (<$IN>) {
   next if $seen{$_}++; # check/mark line as seen
   print $OUT $_;
}

close $IN; close $OUT;
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Or, even shorter while loop:

while (<$IN>) { $seen{$_}++ || print $OUT $_ }
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