Negligence is the legal term for any careless behavior that causes, or contributes to, an accident. For example, a person is negligent if he neglected to stop at a stop sign and, as a result, hit your car as you were coming through the intersection.
A person can be considered negligent whenever he or she had a duty to act carefully and failed to do so. (Generally, we all have an obligation to act with ordinary and reasonable care in any given situation -- that is, in a manner that will not foreseeably injure those around us). For example, a person who drove at night wearing sunglasses would be negligent, because any reasonable driver would know that doing so would increase the chances of causing a traffic accident.
For most types of accidents, a person must be found negligent in order to be held legally responsible for another person's injuries. If a person behaves negligently and that behavior causes you harm, you can most likely recover compensation for your injuries.