Why is a nations economy is divided into sectors? I understand that modern economists divide a nations economy into sectors such as such as primary, secondary, tertiary, quaternary and quinary. 

What is the point of such classification?
That is because in science we try to not just create new knowledge but also classify the knowledge.

In biology biologists don’t just study living things they also classify them as mammals, birds etc based on similar characteristics, in astrophysics physicists don’t just study different astronomical objects but classify different astronomical objects into categories such as planets, asteroids, stars etc. based on similar characteristics, and finally in economics we don’t just study an industry but also categorize industries again based on similar characteristics.

The point of such classification is to have established nomenclature which makes subsequent research more easy. If a economist says “I study primary sector in US” the economist does not need to always explain that he or she studies the sector that produces raw materials/agricultural which saves a lot of time and makes process of science as efficient as possible.