The two detainee cases that were decided Monday are Hamdi v. Rumsfeld and Rasul v. Bush. These are two very important cases, because they deal with some fundamental civil liberties, and figuring out what the Supreme Court actually said is worth everyone's time. Here's my attempt to be as clear and succint as possible in summarizing the judgments. In this post I'm just gonna deal with the Hamdi.
Hamdi involves an American citizen (Yaser Hamdi) who was captured (not by the US) in Afghanistan and was alleged to have been fighting for the Taliban. He was therefore detained as an "enemy combatant" (and therefore not subject to the Geneva Conventions, according to the administration) and is being held in a Navy brig in Charleston, SC. Hamdi sought the right to challenge his classification as an enemy combatant in court. The administration argued that Hamdi did not have this right as an enemy combatant and that they could hold him indefinitely at their discretion. They argue that the president's inherent authority as Commander in Chief allows him to designate any person (including an American citizen) an enemy combatant at any time.