Marriage, from the perspective of the state, is a type of contract between two people. Two people enter into the contract under terms set by the state, which affords them certain additional rights and privileges that unmarried people do not have.
Currently, the state says that Joe can enter into this type of contract with Jane, and Jane can enter into this type of contract with Joe, if both Joe and Jane agree.
However, with a ban on gay marriage, the state is saying that Joe cannot enter into this very same contract with John, because John is a male. That's discrimination on the basis of gender, and its unconstitutional.
So, contrary to Republican spin, gay marriage is not about giving "special rights" to a certain class of people, but rather it is about the equalization of rights and putting a stop to gender discrimination.