About 120 New Zealanders will shortly receive a letter from the Governor General. It will in essence say, "I am writing to advise you Her Majesty The Queen has been pleased to award you the honour of [whatever the award is] in recognition of your services to New Zealand. This honour will be announced in The Queen's Birthday Honours List 2018 ..."
On average, I was once told, 10 per cent will decline such an offer. Their reasons, which they don't have to supply, will be various. They will range from their personal dislike of the royalty system and therefore being unwilling to accept an honour from it, to not wanting their usually unpaid work for the community being publicly recognised.
Such awards are usually given not for the work that is their main source of income, but for efforts made on a voluntary basis in their spare time. Therefore someone who has been a Plunket nurse all her life would not necessarily comply. If she'd spent all her free time teaching riding for the disabled, then that would be seen as a good reason for such an award.
The majority of awards emanate from the public. Groups of ordinary citizens who believe one of their colleagues or friends needs recognition write to the relevant parliamentary officer with their proposal, usually endorsed by some local dignitaries, and the system takes it over from there. The business sector or sports organisations also follow this simple course.
The Prime Minister appoints various ministers of the Cabinet to a ministerial committee named the honours and appointments committee. They sort out a list of people they believe deserve recognition and send this to the Queen for her approval. When that is received, the GG sends out those letters.