When you Tap on Contacts, the default view is your list of contacts, but if you tap again on the View title at the top you are presented with a list of alternative views:
Choosing Contacts Near Me results in this Map display:
All the contacts in your database within a defined* radius to your location are represented by a clickable pushpin. Tap once on the push pin to identify the contact, tap again to get to the phone number and tap a third time to dial.
*Radius is configured under settings -> Search Settings - slide bar sets the radius in either miles or km.
This view is also available for Leads!
NOTE - finding this view in the new mobile app - Click on the "map" icon: