The information came via a senior intelligence official.
The emails are reportedly cloned, held for a few seconds on NSA servers, scanned, and then —- theoretically -- deleted if no matching information is found. The senior intelligence official said the NSA makes a “clone of selected communication links” in order to gather the textual communications, which may include both SMS messages as well as emails. However, the official did not specify other details, such as the volume of data that passes through NSA servers.
The surveillance was authorized by a 2008 law, the FISA Amendments Act, in which Congress approved tapping communications made on "domestic soil" sans warrants as long as the “target” of the communication was a non-citizen abroad. However, voice communications are not included in the authorized cross-border data mining operation.
Once the data reaches NSA servers, software searches it for any identifying keywords or other “selectors.” Messages that match are stored for later analysis by humans. The senior intelligence official said the keywords and selectors were “very precise” in nature, to minimize privacy impacts.
That being said, this is just the latest in a string of revelations about NSA domestic spying programs. First reports on these were made via leaks from former NSA contractor Edward Snowden, currently in Russia under "temporary" asylum.