Others have offered explanations and if you'd like another example (perhaps something a little less textbook-like) I just grepped this from my scratch directory. It's hideous, yes, but demonstrates the point at hand.

Newlines added for "clarity":

print LWP::UserAgent->new()->
        request(
                HTTP::Request->new(GET => 'http://geeksalad.org')
                )->content;
[download]

Of course, there's no error checking in there (I didn't want it at the time). That'd make it look a bit more like:

if (($_=LWP::UserAgent->new()->
    request(
        HTTP::Request->new(GET=>'http://geeksalad.org')
            ))->is_success) {
        print $_->content;
}
[download]

I'm assuming, of course, that HTTP::Request isn't going to fail (unlikely anyway). And this doesn't allow me the opportunity to do anything useful with the UserAgent object other than what I could have accomplished with LWP::Simple. I have no idea why this was there, other than to serve as an example of some kind. Whether this was to demonstrate something good or bad, I can no longer remember. :)

This mess is more commonly written as something like (edited from the LWP manpage):

# Create a user agent object
use LWP::UserAgent;
$ua = new LWP::UserAgent;
my $req = new HTTP::Request POST => 'http://geeksalad.org';
my $res = $ua->request($req);
if ($res->is_success) {
    print $res->content;
} else {
    print "Bad luck this time\n";
}
[download]

So what my code snippet above did was exactly what's being done below, except that I don't put the request object into a variable ($req), and I don't put the user agent object ($ua) in one either. The only thing I stash away is the result ($res/$_) object because I have to call two methods (content, is_success) on it. Neither of these returns the original object, so I can't chain these together with ->'s.