Anything that's centralized is under the control of one unified authority or located in a single place, like a centralized government.
If a business is centralized, it operates from a central location, rather than spreading things out between stores, offices, or factories. Managers of satellite offices have less power if they work for a centralized company, where decisions are made in a home office. A centralized government works the same way, with power concentrated in the executive branch. Centralized derives from a Latin word meaning "center" and the Greek root kentron, "sharp point."