MapEver does not transmit or share any data. All data is stored locally on your device.
However the data is not encrypted and no effort is made to prevent for example other apps from accessing it.
The app collects and stores your GPS position while the app is in use. In addition it also stores the map photos it uses.
Should the app start to use data beyond what is described here, it will be mentioned in the update notes ("WHAT'S NEW" in the Play Store).