This is a so called QgsLocator filter, implemented as a QGIS plugin.
Read about writing one here:
http://www.qgis.nl/2018/05/16/english-coding-a-qgslocator-plugin/
This Locator Filter searches for names in the dutch national search service PDOK
https://github.com/PDOK/locatieserver/wiki/API-Locatieserver
You can install this 'Locator Filter' as a plugin by searching for it in the QGIS plugin manager in your QGIS desktop, search for 'pdok':
http://plugins.qgis.org/plugins/pdok_locatieserver_locator_filter/
Some more docs and api's:
http://api.qgis.org/api/master/html/classQgisInterface.html
http://python.qgis.org/api/core/Locator/QgsLocator.html
http://python.qgis.org/api/core/Locator/QgsLocatorFilter.html