From Justice Anthony Kennedy, writing for the majority in United States vs. Windsor:
The class to which DOMA directs its restrictions and restraints are those persons who are joined in same-sex marriages made lawful by the State....This opinion and its holding are confined to those lawful marriages.
In a nutshell, Kennedy says the Constitution doesn't forbid states from banning same-sex marriage. But if a state allows same-sex marriage, the federal government can't refuse to recognize it. Marriage is a state concern—in fact, it's literally a textbook example of a state concern—not a federal one. Taken as a whole, this ruling was as pure a defense of federalism as we've seen in a while.
So why did all the conservative justices oppose it? Answer: Because no one actually cares about federalism. It's merely a convenient veneer when you prefer one outcome over another. Yesterday state sovereignty was of crucial concern when conservatives gutted the Voting Rights Act. Today, they couldn't care less about it.