http://www.royal.gov.uk/MonarchUK/HowtheMonarchyworks/Whatisconstitutionalmonarchy.aspx
Constitutional monarchy is a form of government in which a king or queen acts as Head of State.
The ability to make and pass legislation resides with an elected Parliament, not with the Monarch.
As a system of government, constitutional monarchy separates the Head of State’s ceremonial and official duties from party politics.
A constitutional monarchy also provides stability, continuity and a national focus, as the Head of State remains the same even as governments change.
The Sovereign/Monarch governs according to the constitution - that is, according to rules, rather than according to his or her own free will. The United Kingdom does not have a written constitution which sets out the rights and duties of the Sovereign, they are established by conventions. These are non-statutory rules which can be just as binding as formal constitutional rules.
As a constitutional monarch, the Sovereign must remain politically neutral.
On almost all matters the Sovereign acts on the advice of ministers. However, the Sovereign retains an important political role as Head of State, formally appointing prime ministers, approving certain legislation and bestowing honours.
The Sovereign has other official roles to play such as Head of the Armed Forces.
http://www.royal.gov.uk/MonarchAndCommonwealth/NewZealand/NewZealand.aspx
New Zealand is a parliamentary democracy and constitutional monarchy with The Queen as Sovereign.
As a constitutional monarch, The Queen abides by the decisions of the New Zealand Government, but she continues to play important ceremonial and symbolic roles.
http://www.royal.gov.uk/MonarchAndCommonwealth/NewZealand/NZGovGen.aspx
The Governor-General is The Queen's representative in New Zealand. As such, he or she performs the same constitutional role in New Zealand as The Queen does in the United Kingdom.
The current incumbent is Lt Gen Rt Hon Sir Jerry Mateparae.
The Governor-General has three overlapping roles - constitutional, ceremonial and community-related.
Constitutional roles include receiving the writ that dissolves Parliament before a general election is held; formally requesting the leader of the political party which gains the support of a majority in Parliament to form a government; and assenting to the enactment of legislation.
Ceremonial duties include opening new sessions of Parliament; presenting honours at Investitures; welcoming visiting Heads of State; receiving the credentials of foreign diplomats; and attending Waitangi Day commemorations.
The Governor-General also provides non-partisan leadership in the community, acting as patron of many charitable, service, sporting and cultural organisations, and attending functions throughout the country, from Northland to Stewart Island, and from Fiordland to the Chatham Islands.
Although the day-to-day affairs of state are delegated to the Governor-General, The Queen continues to have a close and personal relationship with New Zealand and her people.
The Queen and Governor-General both send messages to members of the public celebrating notable birthdays and wedding anniversaries.
http://www.royal.gov.uk/MonarchAndCommonwealth/NewZealand/TheQueensroleinNewZealand.aspx
New Zealand is a constitutional monarchy with The Queen as Sovereign.
The Sovereign and the House of Representatives together make up the Parliament of New Zealand.
As a constitutional monarch, The Queen of New Zealand acts entirely on the advice of New Zealand Government Ministers. She is fully briefed by means of communications from her Ministers, and has audiences with them where possible.
The Queen is responsible for appointing a Governor-General for New Zealand, which she does on the advice of the country's Prime Minister.
This is The Queen's personal representative in New Zealand, who usually serves for a term of five years.
The Queen recognises events affecting in New Zealand - for example, sending messages for national celebrations or tragedies. She also honours New Zealand achievements at events in the UK - for example, holding a reception for members of the All Blacks rugby team at Buckingham Palace in 2005.
As Head of the Armed Forces, The Queen holds colonelcies in a number of New Zealand regiments, and commemorates the service of New Zealanders in various conflicts throughout the past century.
When The Queen visits New Zealand, she performs many of the duties normally delegated to the Governor-General - for example, presiding over the opening of Parliament.
She also makes a pointing of travelling widely throughout the islands, meeting New Zealanders from as many different walks of life as possible.
The Queen of New Zealand's formal title is: Elizabeth the Second, by the Grace of God, Queen of New Zealand and Her Other Realms and Territories, Head of the Commonwealth, Defender of the Faith.
In the Maori language, The Queen is known as Kotuku, which means "the white heron", a cherished bird rarely seen in New Zealand.