They ruled that the "Defense of Marriage Act"'s ban on same-sex marriage was unconstitutional.
Um, where did you get that? The act is still in place - states don't have to recognize same-sex marriages. The only Supreme Court ruling that I know of (quick Google search seems to confirm, but I may not have used the right search terms) had to do with California's Prop 8, and the ruling said that you cannot take rights away from a group once they had already been granted. If the Supreme Court had struck down the Defense of Marriage Act, then Utah wouldn't have been able to appeal.
They also stated that one state does not have to recognize what happens in another state, but the federal government does - ie if you are married in California, Texas doesn't have to recognize the marriage as legal, but the IRS does when you list your spouse on your tax forms.
It (mostly) affirmed the constutionality of "affirmative action" in university admissions
Eh, that is a bit of a stretch. In a nutshell, they said that race could not be the only determining factor, gave a list of guidelines, and sent it back to the lower courts.