For now, there are two points that seem interesting. I'm sure more will become apparent on a thorough reading.
First is the holding that the military commissions violate the Geneva Conventions. This is a dramatic thing to say, from a symbolic perspective, but it is less important as a legal matter. Americans care less about international law than do the citizens of almost any other country. But the Geneva Conventions still have a powerful significance to most of us. These were signed after World War II in response to the utter evil that was practiced in that war. Saying that we're violating them symbolically compares us to the Nazis. That's not what the Supreme Court is saying, of course, and it's not logically true that any Geneva Convention violation equates to Nazi-level criminality. But the symbolism is powerful.
The thing that's going to be misrepresented, though, is how international law is applied by U.S. courts. The rule is that international law is functionally the same as a federal statute (putting aside some technical questions like the self-executing nature of a treaty). That means that the courts will apply international law--but it also means that Congress can pass a statute and override international law. That is, the Supreme Court can say, "The United States is violating its international law obligations by doing _______, but since the statute says to do ______, there's nothing we can or will do about it." This is different, obviously, from a constitutional provision, where the Court will say, "The statute says to do ______, but since the Constitution says the government can't do _______, we will strike down the statute."
Invoking the Geneva Conventions doesn't mean the Court is saying that Congress and the president can't have military commissions like this; it is saying that the president can't do this on his own without having a statute that authorizes this sort of military commission. If Congress amended the Uniform Code of Military Justice to permit these commissions, then (presumably) the courts wouldn't (shouldn't) put a halt to the commissions just because they violate the Geneva Conventions. The Supreme Court would be on record as saying that the actions the U.S. was taking were illegal under international law. but they wouldn't do anything about it.
Which leads to...
Second, the greatest legal significance of this decision may be very much overlooked in most of the media coverage and debate. Does anyone recall the discussion during Alito's confirmation hearings about the "unitary executive?" Even when a GOP-controlled Congress was solidly behind him and he had great public support, President Bush has insisted that the Executive has the authority to do all kinds of things without getting authorization from Congress. His legal brain trust, people like Alberto Gonzales and John Yoo, spun theories that said the president could do whatever he wanted in the field of defense and foreign affairs: a staute couldn't stop him from torturing people, and he didn't need a statute to authorize almost any of his actions. This has turned up in all sorts of contexts, for instance the illegal wiretaps.
What today's decision means is that the Supreme Court doesn't buy the Gonzales-Yoo line (though Alito--surprise--dissented). Quaint notions like the separation of powers still matter. This is fundamental to our form of government and to the liberty of each of us. So it's not just about foreigners, or a bunch of guys in a small corner of Cuba.
My quick skimming suggests to me that Bush could actually still create military commissions like the ones he tried to put into place this time--but he'll have to ask Congress to pass a law allowing him to do it. That's terrifically important as a principle, but it will also make for some fascinating politics. Gitmo is becoming more and more of an albatross. Will Bush want to ask Congress to effectively overrule the Supreme Court--and to enact a statute that our highest court has said violates the Geneva Conventions? If he does, will the Senate go along with it? Besides Arlen Specter, will enough GOP senators step out of line to defeat what Bush asks for? If not, will the Democrats have the spine to filibuster? As I say, it could be fascinating.
But, first, I pity those of you living in the U.S., because you're going to have to live through a lot of black-helicopter rantings from the usual suspects before everyone calms down and we get down to talking about what really matters in this decision.