Division: a business unit of a larger organisation. For example, the IT helpdesk of a department would be a division; the Engineering Faculty of a university, the Aged Care unit of a hospital, etc.
Division should be thought of as going hand-in-hand with position title. I.E., the position may be "Assistant Director" and the division may be "Corporate Support Branch". Obviously, these two fields are closely linked.
Division can also be used to indicate the nature of a branch or to expand on someone's area of responsibility - for instance, the librarian in charge of Smithsville Library, South Jameston would have the position, division and organisation of "Library Manager, Smithsville Library/ South Jameston Town Council".