English. ‘Hiberno-’ means ‘Irish’ or ‘relating to Irish’. See Oxford Dictionaries.
The Hiberno-Norse, are also known as Norse-Gael. These terms generally refer to descendants of mixed Scandinavian and Irish ancestry. This occurred when the Vikings settled down and interacted with the locals in Ireland and Scotland and became part of their society. See National Museum Ireland.
It is also one of the terms that is debated in academia for its accuracy. There is a fine article explaining the issues of trying to distinguish so specifically between Norse and Danes in Ireland (or any other place, for that matter).
Related term: (1) Norse-Gael, (2) Gall-Ghàidheil (foreigner Gaels).