A Blockchain is not controlled by a central server or authority and for that reason all “entries” are, and remain, in the network indefinitely, whereas, in a normal database all data is “centralized”, and not “shared”.
Agreement on the history of the database data i.e. checking history of “entries”, is achieved by sharing and restricting the entries and not by a single entity.
Note that the history contains information such as balance, transactions etc.
All agreements on the history are achieved by “Smart Contracts“, depending of course on the technology used by the said Cryptocurrency.
For example, Ethereum uses Smart Contracts, Bitcoin is not. “Smart Contracts” are agreements that have been codified in the Blockchain. For example, if X drops below Z, send $W to John.