Nobody really knows what happens when you see that shut down animation on your phone. Is it still on? Over 18 months, the police have used is the fake cell phone tower. It is a model called the Stingray that acts like a connector. It forces all phones or devices in the area to connect to it. Then it stores the information it will later give to the cops. The police will also sometimes go to phone companies to get information on citizens they think will have traces to crime. Sometimes they will just use brute-force for the information. Another way is for the NSA to keep your phone on and listen to your conversation. Much of this is only to help capture the criminals who do murders or robberies.
Usually, you would not need to care much about this except if you were some criminal.