What do governments do?

I am not really familiar with government or stuff like that, but I know that they do things for their people. I think governments are divide into different categories, and there are law(I don't know if they call it like this or other name), education, economic, health, and some other important things. For education, I think they just set of some rules that kids should do, like kids under some age needs to go to school for sure. Sometimes educational office people also event dances that are healthy for kids, and they just teach the wellness teacher in every school, and then students has to learn it and dance at least 2 times per week in school. For health, I think they just have to tell people to be aware of disease, and tell people what to do to avoid that. For law, I think they make just make laws, and the people that works for the government will vote, if it pass more than half, then the law will be establish and people will have to follow it.
For economic, they think of ways to turn economic good and smooth. I think that's all I know about government for now, I am totally not sure about it, but that's what I have in mind. :D