Charter schools are very, very popular in our district. Many new ones are proposed each years. For us, the schools are still public school receiving public funding, but don't have to follow the district rules. They set their own charter, hence Charter Schools. But they do have to provide their own building, and all the other stuff that goes into school. Teachers have to be approved by the school board. However, district rules do not always apply to charter schools when it comes to teacher hiring. For instance, some of the schools here use computer professionals from the community to teach computer science classes even though they don't have their official teaching credentials. Teachers in the district schools have to follow state mandates for certification.
Many schools are set up with a specific curriculum/focus that some teachers and parents prefer to the district curriculum.
We have few Core Knowledge schools, a music and arts school, a couple of dual immersion (spanish/english) schools, a montessori etc.
Parents choose these schools because they offer a different curriculum that may fit their child better than the standard district curriculum. I chose a core knowledge curriculum for two of my three children because it suited their learning styles better. The third child did the district curriculum because it suited her style better.
Districts tend to not like them, since they draw children out of the schools, taking their funding with them. Our school board argues that it dilutes the funding too much. Our district tried to put a cap on charter schools, but lost a state lawsuit.
Hope this helps!