In divisional organizations, the required business functions are grouped by product or geography, or some other common theme:
(from http://www.vertex42.com)
Here, the obvious advantage is that product ownership is explicit - everyone in the division is responsible for making sure the product is defined, designed, manufactured and supported. There is less competition for resources across products and at least in theory there should be less siloing among the business functions for a product. There will be competition between the products for resources, and there can be a lot of duplication and waste in having multiple business functions (like Accounting or Customer Service) for each line of business. In some organizations, the common business functions might be removed from the product line and placed in a common 'pool'. One big disadvantage to divisional organization is that it can be hard to advance your career across the business lines and if the departments are small, the opportunities for promotion might be limited.
Companies that have grown by acquisition will frequently have a divisional organization, because it is easier to just make the acquisition a separate division than to try and integrate it into the existing company. It is also easier to spin-out (sell) a fully functional division as a separate company.
