Standing is basically the legal right to initiate a lawsuit. The appellants here are not directly involved in the conflict that was raised, the issue was between the plaintiffs and the State of California. A reasonably understandable definition can be found here. The appellants have to convince the 9th Circuit that they be allowed to intervene in the face of the State's inaction, either as public advocates for an act of direct democracy *which would probably be granted if no government authority wanted to intervene* or as organs of government in the State who have responsibility for administering the law *county clerks' offices, some municipal governments, etc.* A number of counties petitioned to intervene when the case was first being heard by Judge Walker and he pretty much ignored them, and they're making petitions again now to the 9th Circuit who probably won't ignore them since the State itself has bowed out. The decision to not grant/recognize standing can itself be appealed as well.