A civil wrong is a wrong that is not a criminal act, but that creates a cause of action for a lawsuit. A tort is a common example of a civil wrong.
If a person believes that a civil wrong has been committed against them, then they can file a lawsuit against the party who they believe caused the civil wrong.
In such cases, people who file the lawsuits and make the complaints are known as plaintiffs. The people who are defending themselves against the complaints are known as defendants.
If a plaintiff wins the case, then the defendant can be forced to pay damages to the plaintiff. Damages are typically sums of money that are usually proportional to the amount of money lost by the plaintiff due to the occurrence of the civil wrong.