Here are the links that I am using as sources:
These explain our beliefs on the matter very well. I will try to summarize:
We believe that the family is a central unit of society and also essential to God's plan for all of His children. God instituted the family among mankind from the beginning, with Adam and Eve together as our common parents. For this reason, we believe that it is essential that marriage be defined as the union of a man and a woman. This is the standard that God established and we uphold that standard.
Here are some things that we do not believe:
We do not believe it is acceptable before God to discriminate against anyone based on their sexual orientation. Hate crimes are a serious sin. Bigotry in all its forms is unacceptable before God, because He is the Father of all. The Church's purpose in supporting Proposition 8 was not to persecute anyone, it was to support a path for society that we believe is stable and acceptable before God. Please remember the following:
Even more, the Church does not object to rights for same-sex couples regarding hospitalization and medical care, fair housing and employment rights, or probate rights, so long as these do not infringe on the integrity of the traditional family or the constitutional rights of churches.(from the first link I posted)
What the Church is opposed to is changing the definition of the family. That is why the Church supported Proposition 8. Furthermore, a Church is completely justified in speaking out politically. The separation of Church and State is something I hold dear. Everyone should recognize how important that separation is. It would be awful if there were a state religion, no matter what religion that would be. A Church expressing its views and asking its members to defend a central principle in no way mixes the two, it is simply political activism, a principle central to American government.
It upsets me that people are protesting in front of temples in California and other places. For one thing, I don't understand why our church is singled out, when we were part of a coalition of churches that supported the measure. There was an extremely distasteful commercial shown in California that labeled Mormons as home invaders who were coming to take away your rights. It seems very ironic that people labeled us as home invaders and then went to disrupt our worship services. I don't think its appropriate to disrupt someone's worship (which is a protected Constitutional right) because you disagree with their views.
In closing, I would like to say that our Church isn't about hate or discrimination. We merely believe that marriage and the family play a central role in God's plan and also in society. There never has been a successful society that wasn't based on the traditional family. We are trying to protect our views and rights, not destroy anyone else's. I know that not everyone agrees with me. We do not have to agree, but please do not attack our Church for defending our standards.