This writeup is unabashedly USA centric. Also, IANAL.
Wrongful death is a claim that can be filed against a person for allowing a death that they had the power to prevent. It is an aspect of civil law, as opposed to criminal law, and is thus generally enforced by lawsuit rather than imprisonment. The criminal law equivalent is, roughly, involuntary manslaughter.
The exact definition of wrongful death varies from state to state, but it was originally intended as a means for widows and orphans to collect support when the breadwinner of a family was killed through neglect. It has expanded since its inception, and some states will allow wrongful death suits for immediate family members (including children, both biological and adopted), life partners and putative spouses, and anyone who was financially dependent on the deceased. It is less common for more distant family members, such as siblings and grandparents, to be allowed to bring such suits, but some states do allow this. In some states anyone who suffers financially can bring suit.
In order to sue for wrongful death, the survivors must prove that the acts or omissions of the defendant were the proximate cause of the decedent's death -- in other words, the defendant's actions must have led through a direct series of events that clearly caused the injury.
It is common for wrongful death suits to be brought against the persons at fault for automobile accidents, medical malpractice, poor design, or lack of safety precautions. Wrongful death suits may be brought for either intentional or unintentional acts (negligence), but the exact provisions of who can sue for what are highly variable, and somewhat labyrinthine, so if you find yourself involved in such things it is best to hire a lawyer.