Ummm,
So we get two votes, one for the party, and one for the electorate (area/region/district). These might be for the same party or they might not.
MPs are either representing an Electorate or they are List MPs (chosen by the party).
Our parliament comprises 120 MPs (Members of Parliament) and the balance of these is determined by the party vote. So National got about 47% of the votes so they get 47% of the MPs (or about 54 MPs). Greens got 5.9% so they get this proportion or 7 MPs (etc). In this election the following parties got MPs into parliament (National/Labour/NZ First/Greens/Act)
To form a government you need a majority. So National does not have one - they need Coalition Partners to get over 60 seats, Labour and the Greens together cannot form a government on their own because their percentage is also under 50% . So parties work together/make a deal to try and form a government. The two most likely scenarios are National/NZ First or Labour/Green/First but there are other less likely options too.
The leader of the government (whether it is a single party or a coalition) becomes the Prime Minister/Leader. We do not vote separately for this position so in the last electoral term the leader of the National Party who was Prime Minister stepped down and the Deputy took on the role.
There are pros and cons to this system (it is similar to in Germany) but the positive aspect is that a vote for a minor party still counts, and we have a more diverse parliament.
This is a pretty simple explanation and I have missed a few things out but I hope it makes sense Rachy!!