A database management system (DBMS) is software that allows users to create, manage, and access databases. It provides advantages like reducing data redundancy, eliminating inconsistencies through centralized control, ensuring data integrity, and allowing data to be shared and accessed by multiple applications and users. Key concepts include primary keys to uniquely identify records, foreign keys to link tables, and relational databases having structured relationships between tables compared to flat files. Popular DBMS vendors include Microsoft Access for desktop databases.