The majority used the idea of an evolving "national consensus" concerning "standards of decency" re: cruel and unusual punishment. There was also discussion regarding the emotional capacity of minors to make decisions in an adult manner, and how problematic making a legal decision on that matter is. Additionally, there was a consideration of "international consensus" regarding the execution of juveniles. The US has been alone in the world for the last three years in permitting this practice.
The Right naturally went nuts over the "national consensus" and especially the "international consensus" parts of the decision. Scalia's dissent reads like the delusional wingnut that he is; at one point he claimed that since the execution of children as young as seven was not considered "cruel and unusual" at the time the Constitution was penned, then there is no constitutional reason to prohibit such practices now.
O'Connor wrote a separate dissent where she went to some trouble to make sure everyone understands she thinks Scalia is nuts, even though she came to the same legal conclusion as he did. Very entertaining reading:
http://supct.law.cornell.edu/supct/html/03-633.ZO.html