The Danelaw was the term used to describe Scandinavian England following the Viking conquests by the Danes. The term ‘Danelaw’ itself comes from an early eleventh century description, Dena lage, which has been modernized. Historically, people have defined it many different ways. The way I understand it personally agrees most with historian Gwyn Jones in A History of the Vikings, (1968: 421):
The Danelaw was by name and definition that part of England in which Danish, not English, law and custom prevailed. It comprised the Danish conquests and settlements in Northumbria, East Anglia, the Five Boroughs of Stamford, Leicester, Derby, Nottingham, and Lincoln, and the south-east Midlands.
Historian Cyril Hart’s definition compliments the one that Jones gives us. In his work, The Danelaw (1992: 3) he describes the Danelaw as:
…those parts of England in which the customary law observed in the shire … and in the smaller units of local administration exhibited a strong individuality, arising from the Danish influences which prevailed there.
All in all, historians generally agree that once the Danes had conquered the listed regions of England and settled, they assimilated by re-creating their own Danish culture in their newly won land, which was ruled by Guthrum during the time of Alfred the Great.