Schools are used to increase the education of citizens. Educated citizens will produce more resources in any profession/professions they may be assigned to. A school house requires a teacher to be assigned as a worker before children can be educated.
At 10 years old, a child will either start working or, if there is space in a school that is staffed by a teacher, they'll become a student for several years. After a certain amount of schooling, they'll become educated workers. The length of schooling depends on how much time they spend at the school (affected by how far from their house it is), and they will become educated when they are between 17 and 24 years old.
If a child doesn't have a school to attend, they'll become an uneducated worker, having forever missed their chance to be educated.
If a teacher is removed from a school while students are attending it, the students will try to find another school to attend. If there is no school for them, they will become general laborers that are uneducated.