Private law is the area of law that deals with the interactions and relationships between individuals, companies and associations. This is an alternative to public law, which deals with interactions between citizens and the government.
Torts between citizens are generally considered to be classified as falling under the realm of private law.
Despite the fact that private laws do not involve a citizen's relationship with the government, all citizens are expected to act in accordance with private laws. If a citizen disobeys a private law, then they may find themselves a defendant in a lawsuit.
For example, if a person causes thousands of dollars of damage to a plaintiff's boat and refuses to pay, then they may be sued by the plaintiff for damages.