Bureaucracy is a form of government in which a professional class manages the day-to-day operations of the government. They collect the taxes. They build the roads. They turn the ruler's wishes into actuality. The Chinese mandarins are an early example of a bureaucracy. The motor vehicle agency of your local government is a later example.
Bureaucracies provide a certain amount of stability and competence to a government, ensuring that the government will continue to operate efficiently even if the old ruler is thrown out and a new and totally inexperienced ruler takes his or her place. Over time, though, a bureaucracy may become "entrenched" - growing in size and inefficiency to the point where it is extremely difficult for a leader to accomplish anything - good or ill.