To decentralize is to move control from one big organization to several smaller ones. A bookstore chain might decentralize by shifting from one main buyer purchasing books for all the stores to individual store buyers making those purchases.
In government, the term decentralize is used when authority moves away from federal control to the state — or from the state to a local level. Your state, for example, might decentralize laws about stores using plastic bags by allowing each city or town to make its own rules. In business, a company decentralizes when it gives more control to individual locations (like the freedom to hire workers and make rules), rather than making these decisions for them.