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.