Under law, negligence is usually defined in the context of jury instructions wherein a judge instructs the jury that a party is to be considered negligent if they failed to exercise the standard of care that a reasonable person would have exercised under the same circumstances. In most jurisdictions, it is necessary to show first that a person had a duty to exercise care in a given situation, and that they breached that duty.
In brief: Negligence, a tort, is a civil wrong consisting of five criteria: Duty or reasonable standard of care (as decided by judge as a matter of law), Breach (or "negligence" in laymen's terms, decided as a matter of fact), Injury (the fact that the plaintiff suffered an injury, and is determined at a matter of fact), Cause in Fact or conduct of defendant that causes plaintiff's injury(s)(decided as a matter of fact), Legal Cause (now perceived as the foreseeability of the type of injury caused but not the specific injury or extent of injury, determined as a matter of fact). Matters of law are decided by a judge, matters of fact are decided by a jury.
In order to prove negligence, it is not necessary to prove harm, but in order for a cause of action to rest in tort, harm must be proven. Hence, it would be meaningless to sue someone for negligence if no harm resulted. Conversely, it is not enough that a harm was done. In order for the harm to be compensable in a negligence lawsuit, the defendant must be shown to have been negligent, and it must be demonstrated that his negligence was the proximate cause of the harm sustained by the plaintiff.