The US and Canada had fertile land and furs, India had popular consumer goods such as tea and spices, Africa had precious metals and exploitable populations, and Australia was barren but was a very useful penal colony. However New Zealand seems to lack any significant draw for the British Empire, so was their a specific reason I am not aware of, or was it simply a matter of "Empire"?
Basically for the possibilities of natural materials. New Zealand is a little bit larger than the the UK and a small indigenous population, and a temperate climate, so it became of huge agricultural importance. New Zealand proved to be profitable with a lot of wool (distancing dependency on the US), sheep, but most importantly, gold.
Basically any time you start a settler colony it's a gamble. It was a far bigger gamble to have started a penal colony on Australia, and then claim half the continent/island.
The "British Empire" did not really "colonize" New Zealand. The colonization was begun by private enterprise, and the British government stepped in later to ensure order and protect (to some degree) the rights of the Maori inhabitants.
An organization called "The New Zealand Company" was founded in 1825 to trade with New Zealand, buy land from the Maoris, and sell it to settlers. They tried to get some sort of charter or authority from the British government, but failed.
They sent two ships and bought some large tracts of land, but abandoned attempts to trade or settle colonists.
In 1839, the New Zealand Company was resurrected with new money (again trying but failing to get a government charter). Again, they bought more land from the Maoris, and nine immigrant ships headed for New Zealand. By this time, some 2,000 British subjects had already settled in New Zealand in un-organized colonization.
In 1840, the British government became dissatisfied with the scramble for land in New Zealand, and worried about chaos and conflict between settlers and the Maoris. They were perhaps even more worried by reports of a French company setting up to create a French colony in New Zealand. The British sent an official delegation, which negotiatied the "Treaty of Waitangi" with various Maori groups, which established British authority over New Zealand.
The British government then unwound various (but not all) land purchases from the Maoris by the New Zealand Company, which the British deemed to have been dubious or fraudulent, and forbade all further sales of Maori land except to the Government.
So, as with many other British colonies. The colonization of New Zealand was not exactly an objective of the British Government or the "British Empire". The colonization was already happening before the Empire got involved. The reason the "Empire" got involved was to try to create order in a disorderly process, to try to protect the rights of the Maori, and to prevent the French from any nefarious designs they might have had on New Zealand.
In other words, it was essentially another "accidental" acquisition of the British Empire, just like many other colonies had been before.