A nation is a lot of people. Apart from that, the word can mean many different things. Sometimes you just think of a larger group of people you see.
But often the word stands for a much larger crowd of people. This can be all the people who live in a country. Most of them are the "people of the state": they have citizenship of that country: That means, for example, that they have a passport of that country and can vote. When a constitution speaks of the people, it means the people of the state. The other people in the country are considered foreigners, even if they have lived there for a long time or were born there.
Sometimes a people means people who have something in common: the same culture, language, ancestors or history. Another word is "ethnic group". An ethnic minority is people who live in a country where their people are not the majority.
What such people really have in common may be slightly different per people or even per person. Thus, one can belong to one people even if one's parents or grandparents come from a different people. In Finland, some citizens speak Finnish and other citizens speak Swedish: but despite the different languages, they all see themselves as Finns.
There is another meaning for the word people: the people are the ordinary people, those who do not have so much to decide. In the past, you had the king and the nobility on one side and the people on the other.