Okay kiddo, so imagine that you and your friends get together to play a game. In the game, you all take turns being the leader, and the other players have to follow the leader's instructions.
Now imagine that the grown-ups in New Zealand play a similar game, but it's not just for fun - it's to show respect and appreciation for people who have done important things for the country. They give special titles, called "honours," to different people who have done different kinds of important things.
But since there are lots of different honours, like "Sir" or "Dame" or "Order of Merit," they need a system to decide which honours are more important than others. This is where the "order of precedence" comes in.
It's like a big list of all the different honours, with the most important ones at the top and the least important ones at the bottom. So if someone has been given the honour of "Dame" which is higher up the list than "Member of the New Zealand Order of Merit", everyone has to show more respect to them for their accomplishments.
Does that make sense, kiddo?