Medical costs
Emergency healthcare is free in New Zealand, but you still might have to pay for other health-related things. Travel insurance with medical cover can help you out with that.
Cancellations
If you need to cancel your trip, your policy's travel cancellation cover can help here.
Baggage
If your personal possessions are damaged, stolen or lost while you're away, your policy's baggage cover could help here.
Emergency repatriation
If you need to be returned to the UK for medical treatment, your policy's repatration insurance could help here too. Without insurance, this could cost thousands of pounds.
Travel disruption
If weather or something else grounds your flight, travel insurance could help here too.