Generally taken to mean the form of Christianity within the Celtic-speaking lands. This is not to mean that there was a single coordinated for of Christianity within these lands at the time. As Patrick Wormald has commented: “One of the common misconceptions is that there was a Roman Church to which the Celtic Church was nationally opposed.”
In Anglo-Saxon England differences between the Celtic Church and the Roman Church included the nature of the tonsure and the date of Easter.
These differences were settled at the Synod of Whitby in 664 when King Oswiu decided that Anglo-Saxon Northumbria should follow the Roman Church.
Amphibalus baptizing converts.
From The Life of St. Alban: (Wikimedia)