The Danelaw was the area subject to Danish rather than Mercian or West Saxon law.
Broadly speaking, the Danelaw was the area conquered by the Vikings in the ninth century. A treaty between King Alfred the Great and the Danish leader, Guthrum, defined a boundary which is roughly the line of the modern A5 between London and Chester, with King Alfred's territories to the south and west, and Guthrum's to the north and east. This boundary, however, was not stable, and some areas were only briefly under Viking control and show modest signs of their culture. The Danelaw was a cultural, not a political unit; and its culture was far from uniform.
Although the word Danelaw does not itself occur in Domesday Book, there are plentiful signs of Viking influence there. The names of territories, institutions, persons, and places were all affected to varying degrees, as was the language of assessment for military service and taxation. The Hundred, hide, and virgate of the south and west become the Wapentake, carucate and bovate of the north and east, for instance; and all place-names ending in -by, and many ending in -thorpe, are among the characteristic signs of Viking influence. Even the peasant classes and the prevalent types of manor in the Danelaw were distinctive.
Leslie Abrams, 'Edward the Elder's Danelaw', Edward the Elder, 899-924, edited by Nicholas J. Higham and David H. Hill (2001), pages 128-43, is a useful review of the varying definitions of the Danelaw. F.M. Stenton, Types of manorial structure in the northern Danelaw (1910), is still the most thorough examination of the characteristic manorial structures of the Danelaw, superseded only in some points of detail; Cyril R. Hart, The Danelaw (1992), provides a detailed analysis of much of the Domesday evidence; and two recent works, Dawn M. Hadley, The northern Danelaw, its social structure, c.800-1100 (2000), and Cultures in contact: Scandinavian settlement in England in the ninth and tenth centuries, edited by Dawn M. Hadley and Julian D. Richards (2000), between them survey all important aspects of the Viking settlement and its legacy in the most Scandinavianised part of the Danelaw.