Can you explain what  my @file = <DATA>; does?

Can you explain what  s/$Npod/$N$1$n/s for @file; does?

At what point does $_ contain multiple lines?

Basic debugging checklist, $_ never contains more than one line

my @file = <DATA>; - assigns the text from the file to an array.
s/$Npod/$N$1$n/s for @file;

- replaces N<..(some text)..>

with <font class="footnote">..(some text)..</font>

and this is the problem... It does not work :(

I think the anonymous monk was wanting you to think in more detail about what the following does:

s/$Npod/$N$1$n/s for @file;
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You might write that in longhand as:

foreach my $line (@file) {
   $line =~ s/$Npod/$N$1$n/s;
}
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In other words, it's acting on one line at a time. The only pod footnote in your example input was split over multiple lines.

package Cow { use Moo; has name => (is => 'lazy', default => sub { 'Mooington' }) } say Cow->new->name