A "domestic partnership" is a category that came into existence when California did not recognize same-sex marriages (and even banned them directly for a time under Proposition 8). It is almost entirely equivalent to a marriage legally but simply applies to persons of the same gender and has a different name.
However, there is a little bit of difference between domestic partnerships and marriages when it comes to ending them. Divorce filing is limited by residency issues alone, while with domestic partnerships, you can only get them dissolved in California if they were first established in California OR if at least one of the parties has resided in California for sufficient length of time.
Although the de facto overturning of Prop 8 by the U.S. Supreme Court basically makes domestic partnerships unnecessary; yet, the law is still on the books and still creates legal situations for those establishing or dissolving such partnerships.