Definitions
Britannica: Bureaucracy.
. . . specific form of organization defined by complexity, division of labour, permanence, professional management, hierarchical coordination and control, strict chain of command, and legal authority. It is distinguished from informal and collegial organizations. In its ideal form, bureaucracy is impersonal and rational and based on rules rather than ties of kinship, friendship, or patrimonial or charismatic authority. Bureaucratic organization can be found in both public and private institutions.
LII: Bureaucracy.
Bureaucracy is a term composed of bureau (meaning "writing desk" in old French) and -cracy (meaning "power" in Latin). A bureaucracy is a form of work organization. The historical meaning of the term refers to a body of non-elected government officials, but is nowadays understood as an administrative system used by corporations and public institutions.
Some critics explain that the formalism of bureaucracy can lead to a heaviness and rigidity of administrative action, and even a monopolization of power for the sole benefit of the interests of bureaucrats (those who work within a bureaucracy).
Wikipedia: Bureaucracy.
. . . a body of non-elected governing officials or an administrative policy-making group. Historically, a bureaucracy was a government administration managed by departments staffed with non-elected officials. Today, bureaucracy is the administrative system governing any large institution, whether publicly owned or privately owned. The public administration in many jurisdictions and sub-jurisdictions exemplifies bureaucracy, but so does any centralized hierarchical structure of an institution, e.g. hospitals, academic entities, business firms, professional societies, social clubs, etc.
Various commentators have argued for the necessity of bureaucracies in modern society. The German sociologist Max Weber (1864–1920) argued that bureaucracy constitutes the most efficient and rational way in which human activity can be organized and that systematic processes and organized hierarchies are necessary to maintain order, to maximize efficiency, and to eliminate favoritism. On the other hand, Weber also saw unfettered bureaucracy as a threat to individual freedom, with the potential of trapping individuals in an impersonal "iron cage" of rule-based, rational control.