It's creating an anonymous array, just like

%hash = map {$_ => undef } qw(city state country);
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which produces a list like

( 'city' => undef, 'state' => undef, 'country' => undef )
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which is then turned into a hash. In fact, any other value than undef would do just as well, as it isn't actually used.

But, it does so for every loop, just to test if $field is one of qw(city state country). That's a very inefficient way of doing it.

A better way would be to create the hash outside of the loop:

my %skip = map {$_ => undef } qw(city state country);

foreach my $field (param) {
  next if exists $skip{$field};
  foreach my $value (param($field)) {
     #process non blank thedata variable
     ...
  }
}
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Or, IMO perfectly acceptable for small skip lists and/or few parameters:

foreach my $field (param) {
  next if grep { $field eq $_ } qw(city state country);
  foreach my $value (param($field)) {
     #process non blank thedata variable
     ...
  }
}
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Note that I moved the test outside of the inner loop, as the result won't change for whatever values you get.