Officials in Texas, Mississippi, and Louisiana had declared that same-sex marriage would not come to their state until the 5th Circuit Court lifts its stay. The 5th Circuit has now done so. In Louisiana, because a District Court had ruled against same-sex marriage the orders from the 5th Circuit must go through that District Court. The District judge has until July 17th, though he was urged to resolve the issue as fast as possible. Some Louisiana clerk offices are giving licenses to same-sex couples anyway.
In Alabama, the state has been battling a District Court order from earlier this year. The federal judge had ruled for equality and several state judges had done all they can to say the federal ruling didn't apply to them. The federal judge has now said the Supremes say it does apply. Get to it.
Even so, as Rachel Maddow points out, several local officials across the South are still kicking and screaming and individual court actions may be necessary.