The address book is stored in your local storage of device or browser. That means the information is not shared to any external service. It can be accessed via the side bar in the web interface and via "Settings" in the iOS application.
Export
The export button can be found in the top right corner of your screen, next to the create entry button.
This will give you a csv file with all your address book entries.
In the iOS application you can export the entries via the drop down menu in the right upper corner ("Export entries"). When copying the data, the address, the name you saved the address under, and the chain ID will be copied and will be exported.
Import
The import button can be found in the top right corner of your screen, next to the create entry button.
After selecting a file and clicking the import button, your existing address book will be updated.
In the iOS application you can export the entries via the drop down menu in the right upper corner ("Import entries"), here you can choose between "Recents", "Shared", and "Browse" to choose the relevant file.
Existing entries with the same address will be updated with the names from the file.
Existing entries with an address that does not occur in the file will not be touched.