A DBMS is a software package that controls the creation, organization, storage, retrieval, sharing, and security of data in a database. It allows for multi-user access and uses query languages to search, sort, and retrieve data. There are several data models including hierarchical, network, relational, multidimensional, and object models. A DBMS is used in many applications such as banking, airlines, universities, sales, manufacturing, and more. It provides advantages like representing complex relationships, controlling redundancy, and sharing data across applications but also has disadvantages such as complex design, high costs, and required training.