A database management system (DBMS) is software that manages databases, allowing for the organization, storage, and retrieval of data. It includes features such as a modeling language, a query language, transaction controls, and security mechanisms, with various types such as hierarchical, network, relational, and object DBMS. The relational model, introduced by Edgar Codd, revolutionized database management by using tables and keys to link related records, providing flexibility and efficiency in data management.