The use of the term "assault weapon" is meaningless and vague in a way that will make it very difficult for states and localities to enforce blanket restrictions. Many such restrictions appear to me to have been drafted in such a way as to define "assault weapon" as anything that simply looks like a military-style gun (scary, that is), regardless of the fact that millions of people own civilian-version (semi-automatic) weapons such as M4A3/4s, AR-15s, and AK-47s.
I will suggest to you, based upon my quick scan of the 60+ page majority opinion that such bans are going to be much harder to enforce now.
Finally, the Court addresses Justice Breyer's dissenting opinion, in which he argued in part that the D.C. gun ban was supportable because handgun crime was a big problem in the District. Scalia slaps him down pretty hard, and makes a telling point about the right to keep and bear arms (emphasis is mine):
"We know of no other enumerated constitutional right whose core protection has been subjected to a freestanding 'interest-balancing' approach. The very enumeration of the right takes out of the hands of government—even the Third Branch of Government—the power to decide on a case-by-case basis whether the right is really worth insisting upon. A constitutional guarantee subject to future judges’ assessments of its usefulness is no constitutional guarantee at all. Constitutional rights are enshrined with the scope they were understood to have when the people adopted them, whether or not future legislatures or (yes) even future judges think that scope too broad.
Very good news, as I said.
As the Court's 2003 Texas v Lawrence struck down clear precedents of multiple millennia, and it's own clear ruling about privacy rights in 1986 Bowers v. Hardwick so too is this ruling good only until cancelled, and it may be cancelled at whimsy.