Bureaucracy can be relevant to both private and public organizations in ways that are good or bad. Bureaucracies can help large organizations function more effectively. On the other hand, they can cause organizations to become tangled in red tape and therefore less responsive to the needs of those they serve.
Bureaucracy can help large organizations function. Once an organization gets to be fairly large, it is no longer possible for one boss to effectively supervise everyone. The organization then needs to develop a bureaucracy. It could have, for example, different departments that are in charge of different things. Each department could have its own head that reports to the overall boss of the organization. That way, each department can be run by someone who is able to give it his or her full attention (which the overall boss cannot do). The overall boss can control the general direction that the organization is going by giving orders to the department heads, but he or she does not have to do everything. This sort of thing makes an organization more efficient.
However, bureaucracy can also harm an organization. If there are too many levels of bureaucracy, it can be hard for the overall boss to impose his or her will on the organization. By the time orders come down through all the bureaucrats to the bottom of the company, they are watered down and garbled, making it harder for the overall boss to be in charge. Perhaps more importantly, too much bureaucracy leads to too much red tape. Bureaucracy depends on having explicit rules that everyone follows without exception. If there are too many levels of bureaucracy, there get to be too many rules. It gets to where it is too hard to do anything because there are too many forms to be filled out and rules to be followed. This can make an organization unresponsive to the people it is trying to serve. Instead of helping them, the employees will spend more time worrying about following bureaucratic rules.
In these ways, bureaucracy can help or harm public or private organizations.