It refers to lasting harm done to the body, human or otherwise, although in its legal sense it is exclusively defined as lasting harm done to living human beings. It deliberately does not admit social, ideological or psychological concepts of violence, but would admit forms of property damage that a reasonable person would consider likely to cause lasting bodily harm, e.g. to turn off a pacemaker or respirator, or eject someone into a cold wilderness in winter with no other source of shelter.
Police actions are usually defined as those motivated by reducing bodily harm to "innocent" victims, even if violence or property damage is required to do so. The definition of "innocent" is of course dependent on an ideology or due process of law. In general, police also seek to reduce bodily harm done to suspects as well, although this is a lesser concern, much less in some societies.
Doing bodily harm outside the legal process of a given society is usually considered crime, war, or "terrorism", a 20th century term describing various styles of guerilla and asymmetric warfare. In general public opinion in the developed world does not support definitions of war or "terrorism" that do not refer directly to doing of bodily harm.
Systematically reducing, channelling, or eliminating deliberate bodily harm from human public relationships is the focus of political science.