The majority held the refusal of a state to allow or acknowledge same-sex marriage was a denial of the right to due process and to equality before the law. Like the protection that the court gave to allow interracial marriages, same-sex marriage is entitled to the same protection.
The minority held that the question of whether or not marriage was limited to the union of a man and a woman was something for the voters to decide, not the court, and that the Constitution does not grant a right of liberty to marry someone of the same sex.
Which reasoning do you agree with?
[Note: a fuller explanation of the majority opinion can be found here and a fuller explanation of the dissenting opinions can be found here.]