A burrow is any biogenic structure that involves excavation of an unconsolidated (nonindurated) substrate by an organism; the process of forming a burrow by an organisms is burrowing but is also generally called bioturbation (literally "life mixing"). Burrows are primarily associated with excavations in sediment; other types of "burrowing," such as digging into soft tissue (i.e., leaf mines made by insects), are actually more properly termed borings because they permanently erode the structural integrity of a consolidated substrate. A continuum of biogenic structures in sedimentary rocks can range from softground to firmground to hardground traces; softground and firmground traces are considered as burrows, whereas hardground traces are borings.
Tracemakers of burrows are represented by nearly every phylum within the animal kingdom. The scale of burrows can range from nematode traces to excavations left by whales interacting with the seafloor. Most burrows studied by ichnologists are made by invertebrates but any property owner who has been affected by the burrowing activities of modern rodents can attest to the impact of vertebrate burrowers.
Burrows occur in every ichnofacies except the Teredolites and Trypanites ichnofacies, which are substrate-dependent ichnofacies and defined by borings. Assemblages of environmentally related burrows typify the ichnofacies concept, which has been a primary model for applications of ichnology.
Further Reading on Burrows:
Bromley, R. G. 1990. Trace Fossils: Biology and Taphonomy. Special Topics in Palaeontology, London, Unwin Hyman, 280 p.
(A new edition of this book is out now but I have not seen it yet.)
Ekdale, A. A. 1992. Muckraking and mudslinging: The joys of deposit-feeding. In Maples, C. G., and West, R. R. (eds.), Trace Fossils. Short Courses in Paleontology No. 5, Paleontological Society, Knoxville, Tennessee, p. 145-171.