a military camp
a small territorial division of a country
the product or result of an action
So why does cantonment mean a military camp?
Since canton means a small divison of a country, and -ment means the result of an actions, cantonment literally means the product of a division of a country. But, there's also an action in the -ment definition that we forgot. So, once again, even mor literally it means the product or result of having (the action) a division of a country. And what would you need as a result of having a small division of a country? A military camp to protect it!
My brother was deployed to a cantonment in Beach City, a division of the United States of Beaches.