To some extent, the definition of domestic violence varies from person to person. However, the general definition of domestic violence is that it is acts of violence or threats of violence that are committed by a person against a member of his or her household or family.
Disagreement with regard to domestic violence comes in to play with regard to what conduct, exactly, constitutes violence and what conduct is acceptable. This is especially true in the case of domestic abuse of children. For example, there is the famous video that has recently come to light of the judge in Texas striking his teenaged daughter repeatedly with a belt. To some, this is domestic violence, while to others it is simply acceptable disciplinary action.
Almost everyone, however, would define actions like those against a spouse (as opposed to a child) as domestic violence. The most agreed-upon definition of domestic violence, then, is that it is acts of violence committed by a person against her or her spouse or domestic partner. Here again, there are disagreements as to how violent or coercive the behavior must be before it can be called domestic violence. To some, even harsh or hurtful words are abuse. To others, grabbing a spouse in a painful way is abuse. To others, abuse does not start until there is actual striking of the victim that could do harm.
So, the general outlines of a definition are easy. Domestic violence is violence committed against a member of one's family. In its details, however, domestic violence is more difficult to define exactly.