The Danelaw, as recorded in the Anglo-Saxon Chronicle (also known as the Danelagh; Old English: Dena lagu; Danish: Danelagen), is a historical name given to the part of England in which the laws of the “Danes” held sway and dominated those of the Anglo-Saxons. It is contrasted with “West Saxon law” and “Mercian law”. The term has been extended by modern historians to be geographical. The areas that comprised the Danelaw are in northern and eastern England. The origins of the Danelaw arose from the Viking expansion of the 9th century, although the term was not used to describe a geographic area until the 11th century. With the increase in population and productivity in Scandinavia, Viking warriors, having sought treasure and glory in the nearby British Isles, “proceeded to plough and support themselves”, in the words of the Anglo-Saxon Chronicle, for the year 876.
Danelaw is also used to describe the set of legal terms and definitions created in the treaties between the English king, Alfred the Great, and the Danish warlord, Guthrum, written following Guthrum’s defeat at the Battle of Edington in 878. In 886, the Treaty of Alfred and Guthrum was formalised, defining the boundaries of their kingdoms, with provisions for peaceful relations between the English and the Vikings.
The Danelaw roughly comprises 15 shires: Yorkshire, Five Boroughs of Leicester, Nottingham, Derby, Stamford and Lincoln, as well as Essex, the Kingdom of East Anglia shires of Cambridgeshire, Suffolk and Norfolk, East Midlands shires of Northamptonshire, Huntingdonshire, Bedfordshire, Hertfordshire, Middlesex and Buckinghamshire; one third of the total area of the English kingdom at the time.
The prosperity of the Danelaw, especially of Eoforwic (Danish Jórvík, modern York), led to its becoming a target for later Viking raiders. Conflict with Wessex and Mercia sapped the strength of the Danelaw. The waning of its military power together with the Viking onslaughts led to its submission to Edward the Elder in return for protection. It was to be part of his Kingdom of England, and no longer a province of Denmark, as the English laid final claim to it.
Update 31 Jul 2013: I removed the broken image links.