maps.app on iOS "follow me" mode without a destination set In stand-alone automotive GPS systems if you just have it on but have not programmed in a specific destination it will show your moving on an active scrolling street map of the road you are on and any roads that are currently within the default zoom area.

So you get a display that shows your car stationary in the middle of the screen with the map moving around you. I found this extremely helpful when I am in locations that I am not real familiar with or just exploring to get the lay of the land. It's also good for finding shortcuts that you were not previously aware of.

If I open Apple maps (or Waze or Google maps...) tap on the locator (Apple maps arrow at top right) to display my current location the map does not follow me. I eventually drive off the displayed map and would have to tap the arrow to re-center the map. Needless to say operating a phone while you are driving is both Not Really Safe and unlawful in many parts of the US.

Is that something that Apple Maps does and I have not discovered how to activate it? Anybody know what that feature is called?
Make sure you have background app refresh turned on for Maps.  

Go to Settings -&gt; Maps and in the Allow Maps to Access section, turn on Background App Refresh and Cellular Data.  

Also, be sure you allow Maps to use your location by tapping Location and selecting While Using the App.

This is what I have done and the app follows me when I move.  I'm not sure if this is the root answer to your issue but it's how I have it setup and it works for me.