A great explanation of the plaintiffs case is contained in the Memorandum in Support filed as part of the motion.
This case is very important for gun rights all over the country, but it is especially so for gun owners in California. This case seeks to establish that "bear" in the 2nd Amendment applies outside the home as well as inside, forcing D.C. to allow some form of carry, either open or concealed, in nonsensitive areas of the city.
Why is this important to California?
The 2nd Amendment already applies to D.C because of the result of the Heller case. A favorable ruling in Palmer would establish a right to bear arms in 2nd Amendment jurisprudence. While it is true that the 2nd Amendment does not apply to California at this time, a favorable ruling in McDonald v. Chicago is expected to change that in just a few weeks.
California law places great limits on the ability of people to be armed in public. Loaded open carry of firearms is illegal in public places of incorporated towns and cities. Unloaded open carry, thanks to AB 1934, will soon be illegal as well. Issuance of carry concealed weapon (CCW) permits is at the discretion of law enforcement, and DOJ statistics confirm that low issuance rate in urban counties. All of which conform that the there is no effective right to "bear" arms in California.
Assuming a favorable ruling in McDonald, a favorable ruling in Palmer will give California residents instant standing in Federal court to sue California due to the unconstitutional restraints imposed by the California laws. The state will be forced to allow some form of carry, even though that requirement will be extremely distasteful to the state government and to urban police departments, especially in Los Angeles, Santa Clara, and San Francisco counties.
The legal ducks are just about all lined up, with only Palmer expected to take a couple of years to get up through the Federal court system. But if and when Palmer is decided favorably, then we will be treated to the spectacle of the ultra-liberal state of California "swallowing a frog".