"Promising to be loyal to New Zealand and its laws when you become a citizen"
When you become a New Zealand citizen, you say a special promise called the Oath of allegiance. You promise to be faithful to the King or Queen of New Zealand and to follow the laws of the country. You also promise to do your duties as a New Zealand citizen.
You say your full name when you make this promise, and you mention the name of the current King or Queen, such as King Charles the Third. You promise to be loyal to the King or Queen and to their heirs and successors, which means the people who will come after them.
You finish your promise by saying "So help me God", which is a way of showing that you are serious about keeping your promise, as explained in the Citizenship Act 1977, specifically s 11.
I, [full name], swear that I will be faithful and bear true allegiance to His (or Her) Majesty [specify the name of the reigning Sovereign, as thus: King Charles the Third, King of New Zealand,] His (or Her) heirs and successors, according to law, and that I will faithfully observe the laws of New Zealand and fulfil my duties as a New Zealand citizen.