Basically you are right. $_ iterates over @skipper, which happens for each element of the @required list. Adding some print statements help show what is happening.

my @required = qw(preserver sunscreen water_bottle jacket);
my @skipper  = qw(blue_shirt hat jacket preserver sunscreen);

for my $item (@required) {
  print "$item\n";
  unless (grep $item eq $_, @skipper) { # not found in list?
    print "skipper is missing $item.\n";
  }
}
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The variable $item has each value from the @required list. In scalar context grep will return the number of times that the expression was true. $_ is an aliases to the element in the @skipper list.