OneIowa website, which I think explains it quite well:
Some have asked what the Court's decision means for religious institutions.Got that?
It's important to know that while the state, its cities and businesses will recognize marriage for gay and lesbian couples, religious institutions will only recognize it if they choose to. Just as some churches are not required to marry a couple that is not a member of their denomination, this decision will not require any religious institution to recognize a marriage contrary to its beliefs.
The Court's decision specifically states, "The sanctity of all religious marriages celebrated in the future will have the same meaning as those celebrated in the past. The only difference is civil marriage will now take on a new meaning that reflects the more complete understanding of equal protection of the law."
We ahve to keep repeating this over and over -- it's like the teabaggers and healthcare reform, they lie about stuff long enough and people start to believe it!