The position or job of a superintendent, who is a person in charge of something, like a school district or a building project.
A superintendency is a very important job that needs a smart and responsible person.
Examples:
The superintendency of the school district is a big job.
She has the superintendency of the construction project.
The superintendency is a hard job.
The superintendency of the park is a big deal.
The superintendency of the whole city is a very big job.
He has the superintendency of the whole town.