A relationship between two or more people in which one or more parties are physically, emotionally, psychologically or sexually abused.
In long-term abusive relationships the abuser(s) typically have a power relationship over the abused, the power relationship can be anything from legal custody (in the case of child abuse) to drug supply (a lover using threats of loss-of-drugs to control their partner) to emotional manipulation (very common) or financial (all of the common property is in a form which the abuser has power over).
Abusive relationships aren't usually illegal in themselves, but many of the actions performed by the abuser(s) to maintain the relationship often are. However, the abuser(s) are often very careful to perform these actions out of sight and not to leave bruises. An abusive relationship can be a legal defense, as in battered women's syndrome, where wives of abusive husbands kill their spouse and claim self defense.