The squid rain is actually a fun reference to the bizarre ending of the comic the show is based on, so if you've only seen the Watchmen movie, you'll probably be extra confused. Watchmen the comic wraps up with super-rich superhero-turned-mogul Adrian Veidt setting off a catastrophe from his lair deep in the Antarctic ice. In order to prevent worldwide nuclear war and to bring the nations of the world together against a common threat, Veidt genetically engineers an enormous, one-eyed squid to be dropped in the middle of Manhattan. The squid triggers a giant explosion and blast of psychic energy, which is designed to convince everyone they're being attacked by aliens from another dimension. (You see it in the show for a split-second in the scene where Looking Glass is interrogating the 7th Cavalry member.) His plan works: By sacrificing the lives of millions, Veidt successfully ends the nuclear standoff, since the nations of the world think they now have something much bigger to contend with.
It's an apropos finale to a comic all about the lengths so-called "heroes" will go to to save people, or uphold the American dream, or protect whatever else they deem worth protecting. Given how close two world superpowers were to toasting the planet (not just in the comic, which came out toward the end of the Cold War), it's undeniable that Veidt saved the world. It's also undeniable that he killed and maimed an untold number of people in devastating fashion. The show will eventually have to contend with the realities of a world that has been tricked into endless paranoia about fake extradimensional attacks, which is part of the price Veidt was willing to pay in exchange for avoiding nuclear disaster.
This explanation doesn't completely solve the mystery of the squid rain, of course; if there aren't any actual aliens from another dimension to guard against, who's dropping all those squids out of the sky? Is it just an uncontrollable side effect from an event that happened decades ago, or is it someone trying to keep up appearances?
There are more pressing concerns in Watchmen than the nature of the squid rain, but its source is central to the origin of the world Lindelof and company are developing. So keep an eye on the forecast in the coming episodes -- at least there will be no shortage of ink supply for anyone who wants to conduct an old-fashioned Rorschach test.