Nothing. It means nothing to me directly. After the judgment nothing changed for me. My wife and I are still married. We can still file taxes jointly. We still have joint health insurance. All the laws that protected us on Tuesday are still valid on Wednesday.
What changed is that other people, including people I know, now have the same. They have the same protections and red tape my wife and I have to deal with. Have fun filing your joint taxes and dealing with your insurance company's spousal coverage issues.
You wanted it you got it, and I am truly happy for you.
NB: I know it isn't all there yet, but enjoy and savour the victory.