The Governor-General is the titular head of New Zealand’s armed forces, separate from the head of state. In fact, the full title of the office, under the Letters Patent 1983, is the “Governor-General and Commander-in-Chief.”
This is a New Zealand curiosity - for example, the Governor-General of Australia is not the Commander-in-Chief of their armed forces. That said, the title itself is ceremonial now. Under the Defence Act 1990:
The Governor-General, by virtue of being Commander-in-Chief of New Zealand, shall have such powers and may exercise and discharge such duties and obligations relating to any armed forces raised and maintained under section 5 as pertain to the office of Commander-in-Chief.
These “duties and obligations” are essential to do what the democratically elected government of the day tells them to do.
The reason for the existence for the title goes back to the Militia Act 1865, an enactment passed during the New Zealand Wars. Governor George Grey became Command-in-Chief over the colonial armed forces then waging war against Maori in Taranaki.
It is still intriguing though that the role is held by the Governor-General, and not the Sovereign, who is head of state.