If you are a resident of New Zealand, you can rely on the public health system for emergency care and treatment for serious conditions. However simply relying on the public system can have its disadvantages. You may have to wait longer for treatment, not get to choose your specialist or if self employed have to take time off when it doesn't suit. If your condition is not related to an accident, you won’t be able to rely on the ACC (Accident Compensation Corporation) to pay for treatment.
So having some private medical insurance can help alleviate emotional and financial stress of not having to wait around for treatment or having to pay for a large unexpected medical bill.