Kevin Drum explains what the phrase means:
The NSA isn't allowed to spy on Americans, but the nature of modern communication doesn't always make it obvious whether a phone call or email is foreign or domestic. This means that in the course of its normal business of spying on foreigners, NSA will inevitably collect information it shouldn't have. Certain rules, called "minimization procedures," define what NSA is required to do when it discovers that it has inadvertently captured a U.S. person in its surveillance dragnet.
At this point, it's far too charitable to assume that the NSA is collecting this information "inadvertently," and misleading to say that "the NSA isn't allowed to spy on Americans," but that isn't a criticism of Drum, who raises similar points later in his post. (Summarizing NSA documents sometimes requires briefly adopting NSA conceits to explain theoretical rules and procedures. Just don't forget: There are times that the NSA spies on Americans without a warrant, and it constantly collects domestic communications knowing it isn't supposed to have some of it.)
So what happens to the communications that the government isn't supposed to have? When they're accurately identified as such -- often that's an NSA analyst's judgment call -- the relevant data is supposed to be destroyed forever. But there are exceptions, when the NSA can keep and store the purely domestic communications of American citizens, and even forward them onto the FBI.
Here's how The Guardian puts it:
...the Fisa court-approved policies allow the NSA to:
• Keep data that could potentially contain details of US persons for up to five years;
• Retain and make use of "inadvertently acquired" domestic communications if they contain usable intelligence, information on criminal activity, threat of harm to people or property, are encrypted, or are believed to contain any information relevant to cybersecurity;
• Preserve "foreign intelligence information" contained within attorney-client communications;
• Access the content of communications gathered from "U.S. based machine[s]" or phone numbers in order to establish if targets are located in the US, for the purposes of ceasing further surveillance.
The broad scope of the court orders, and the nature of the procedures set out in the documents, appear to clash with assurances from President Obama and senior intelligence officials that the NSA could not access Americans' call or email information without warrants.
At a minimum, this makes President Obama's recent public statements look highly misleading, if not outright lies. Says Drum, after parsing the minimization procedure document, "The minimization procedures are fairly strict, but they do allow retention and dissemination of domestic data -- without a warrant -- under quite a few circumstances. 'Threat of harm' is pretty broad, as is 'criminal activity.' The latter, in fact, seems like a loophole the size of a Mack truck. It suggests that NSA could have a significant incentive to 'inadvertently' hoover up as much domestic information as possible so it can search for evidence of criminal activity to hand over to the FBI." Several other objections come to mind, but I presume that, in coming days, we're going to understand these procedures better than we do now, so let's put that line of inquiry on hold.
A significant point remains:
Why are these particular details highly classified state secrets? It's an abuse of the system -- a scandal in itself. What the NSA does with information it collects but isn't allowed to have isn't something that needs to be decided secretly and kept secret by self-interested national-security bureaucrats.
The information doesn't threaten national security at all. It's an appropriate subject of public scrutiny and debate. To take just one example, should the NSA get to keep "information on criminal activity" unrelated to terrorism? I can see the arguments for and against. But it makes no sense to suggest that knowing the rule currently used or debating it publicly threatens national security. And all sorts of other things that ought to be publicly debated have been and remain classified too, so the NSA can do as it pleases. It would still be secret if not for Snowden, who, whatever else you think of him, may well have given up his freedom to tell us.