New Zealand is located at the south-western end of the so-called Pacific Ring of Fire, which is formed by a continuous line of volcanoes and earthquake locations on the periphery of the Pacific Ocean.The Ring of Fire also marks the edges of (mostly) the Pacific Plate, at the junction with other tectonic plates.
See USGS for a map of the Earth's tectonic plates and the Pacific Ring of Fire.

New Zealand is also located along a zone of contact between the Pacific and Australian tectonic plates. It is the motion of these two plates that is largely responsible for both volcanic and tectonic activity in New Zealand.
Read more: at IGNS, also VolcanoWorld

Below the North Island the Pacific plate slides underneath the Australian plate in a movement called subduction, from a line of contact marked at sea further east by the Hikurangi Trench. Volcanism occurs at the surface above the area where the sinking plate reaches a depth of approximately 85 km, and rocks start melting and migrating towards the surface as magma. At present this area is marked at the surface by the Taupo Volcanic Zone, which has been the most active for the last 1.6 million years.
More about: plate tectonics and subduction

Subduction underneath New Zealand started about 26 million years ago. Since then the related volcanic activity has moved southwards: from Northland through Coromandel to the central North Island at present. This is the result of a steepening of the angle of subduction of the Pacific plate, thereby causing the melting zone to retreat southwards.