Wiktionary
n. (context legal English) A year in the reign of a monarch, beginning on the day of accession, the set of which are numbered ordinally. Formerly laws in the United Kingdom were identified in part by the regnal year of the monarch, and this practice is still followed in some Commonwealth countries.
Wikipedia
A regnal year is a year of the reign of a sovereign, from the Latin regnum meaning kingdom, rule.
The oldest dating systems were in regnal years, and considered the date as an ordinal, not a cardinal number. For example, a monarch could have a first year of rule, a second year of rule, a third, and so on, but a zero year of rule would be nonsense. Applying this ancient epoch system to modern calculations of time, which include zero, is what led to the debate over when the third millennium began.
Regnal years are " finite era names", contrary to "infinite era names" such as Christian era, Jimmu era, Juche era, and so on.