You can read much about what that means in California, the 9th district and nationally.
I have maintained that the word "marriage" in and of itself is extremely important and the decision of the court supported that in more than legal terms. Now, New York, I can say this is my "husband," not my "legally registered domestic partner."
I urge you to read the entire decision but especially starting on page 38...
"We are excited to to see someone ask, 'Will you marry me?', whether on bended knee in a restaurant or in a text splash across a stadium Jumbotron. Certainly it would not have the same effect to see 'Will you enter into a registered domestic partnership with me?'. Groucho Marx one-liner, "Marriage is a wonderful Institution, but who wants to live in an institution?" would lack its punch if the word marriage were replaced by the alternative phrase. ... 'Had Marilyn Monroe's film been call How to Register a Domestic Partner with a Millionaire, it would not have conveyed the same meaning..."
One source for the entire decision in PDF is here.