A library is a database of documents. It has a specific purpose and it is organized according to that purpose.
Such traditional paper-based databases, however, have many disadvantages. They require a tremendous amount of physical space. Libraries occupy entire buildings and searching a library is relatively slow. They are also tedious to maintain and an inordinate amount of time is spent ensuring catalogs and shelves of books remain consistent.
Electronic storage of a database helps to address these issues. Computer software exists that enables a user to create, maintain and manage electronic databases.
This category of software is known as a database management system (DBMS). A DBMS acts a broker between the physical database and the users of that database.
A DBMS for a relational system is typically called a relational database management system (RDBMS).