When scientists talk about the probability of us being the only intelligent species in the universe, they always say that "we should see the galaxy filled with life". I never really understood how they meant that. 

Let's assume we're observing Earth from, let's say, 1 light year away. Is there a way to tell that life exists here and it is indeed intelligent? I mean how would you tell if an alien civilization is having 1000+ settlements in multiple planetary systems? What would be the symptoms?

They'd need a huge spaceship crossing in front of a star for us to notice them or something. 

Is there a proper explanation on this? 

Thanks