They mean a nation. One way of dividing up a large, multi-national company is to do it by country.
Other ways are by function or product line. A "matrix" organization recognizes that people do have different locations in different interlocking webs. They are not just strictly in one hierarchy of corporate organization.
You might be an accountant for X product line in Y country.
"Departments" are usually smaller than "divisions," but the names can be interchangeable as well.