Negligence - Breach of the duty of due care
The basis of most personal injury and wrongful death cases is that the negligence of the defendant caused the injuries to the plaintiff. There are two kinds of negligence claims. One is "common law" based on the Duty of Due Care, and the other is based on violation of some statute, such as the Vehicle Code, resulting in injury to the plaintiff.
Every person owes others the duty to use due care under the circumstances to avoid foreseeable injury to others. When somebody breaches that duty and that breach of duty causes injury to somebody else, there is the basis for a negligence claim. For example, if a supermarket has a broken freezer which is leaking a big puddle of water on the floor in the aisle where customers are walking pushing their carts, and one of the customers slips in the puddle, falling and suffering serious injuries, that would be a breach of the standard of due care. The store has a duty to keep its equipment working properly so as to avoid a dangerous condition developing that could result in serious injury.
If a driver runs a red light, or speeds, they would be in violation of the Vehicle Code. If this illegal driving causes an accident and injuries, then the statutory violation would be the basis for the negligence case. This is called negligence per se under the law.
Other wrongs can result in valid claims for injury as well as negligence, such as assault and battery, or other intentional wrongs. Insurance is normally not available in those cases to pay a settlement for the wrongdoer, so many lawyers do not accept those cases due to the difficulty in every collecting a judgment.