Stingray is the code name for an IMSI-catcher, which is basically a fake cell phone tower sold by Harris Corporation to various law enforcement agencies. (It's actually just one of a series of devices with fish names -- Amberjack is another -- but it's the name used in the media.) What is basically does is trick nearby cell phones into connecting to it.
Once that happens, the IMSI-catcher can collect identification and location information of the phones and, in some cases, eavesdrop on phone conversations, text messages, and web browsing.

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