A Relational Database Management System (RDBMS) is defined as a system where data is stored in tables with relationships also represented in tables, introduced by E.F. Codd in 1970. It encompasses various database management functionalities, including data capture, classification, storage, and maintenance, along with the enforcement of data integrity using keys such as primary and foreign keys. The document also discusses data models and the Entity-Relationship (ER) model to represent real-world scenarios and relationships within data.