The Order of Charlemagne is Familypedia's term for the number of generations from Charlemagne (747-814), King of the Franks (i.e. most of Western Europe), to one of his descendants. His children have Order 2; theirs have 3; and so on. See Project Charlemagne/order and Property:Order of Charlemagne for more detail.
The number is calculated using Semantic MediaWiki and generally appears on an individual's sensor page.