Places
Tap the location line on the compass screen to see the 5 places nearest to you and their distances. This lets you easily check that your location was found correctly; if you are not near these places, tap "Find location again".
This list does not need the internet: data for cities with a population over 15,000 comes with the app and the calculation happens on your phone. The same data is used for the country and city lists in Settings → Fixed location.
Data source
Place data comes from GeoNames (geonames.org) and is used under the Creative Commons Attribution 4.0 (CC BY 4.0) licence.