Why should organizations create departments and branches in management?

This question is somewhat confusingly worded, I think.  You won't have departments and branches in management unless and until you have departments and branches in the organization in the first place.  Once these are in place, you will need managers to run them.  So we can talk about why we divide an organization in this manner and then talk about some reasons departments and branches need different managers.
Once an entity begins to grow beyond a few employees, it is usually necessary to divide up the various tasks of the entity.  These might be divided by function; for example, a research and development department, a production department, and a marketing department. Some departments might be included as support as well; for instance, a legal department and a human resources department. An entity can also be organized along geographical lines, with different divisions in different cities, states, regions, or countries. Or an organization can be organized around different products, such as car manufacturers are.  This is necessary because it is the most efficient way to get work done, decentralizing the various tasks in the organization so that each can have specialists in each division and decision-making can occur on the spot. And these are also reasons to have different managers for different divisions. 
A manager of a very small company can be a jack of all trades, knowing enough about everything to keep a company going.  But a company growing larger needs different managers.  Beyond the smallest of companies, there is going to be a need to have different managers who have different areas of expertise to maximize efficiency and effectiveness. If I have a company of three hundred employees, I want someone who is a certified accountant running my accounting division and an attorney running my legal department. I want a production specialist who can figure out why my production line is not running properly.  I also want managers who can make decisions.  One person holding all the reigns is foolish, no matter how much that person wants to micromanage.  It is the manager on the scene who can best judge the situation, or at the very least, be the person who can provide the most full and accurate report. There is also a concept in management called span of control. This describes how many people a manager is responsible for. If a company has one manager for three hundred people, that is too wide a span of control, and the company will not run very smoothly.  We can only be responsible for so much without becoming completely ineffective. 
Our reasons for dividing an organization are grounded in specialization, efficiency, and effectiveness.  Our reasons for providing managers for these divisions are the same, really, allowing for greater expertise, better decision-making, and a realistic span of control.