What is database manager system (DBMS) and which are their elements?

A database management system (DBMS) is system software for creating and managing databases.
The DBMS provides users and programmers with a systematic way to create, retrieve, update and manage data.

A DBMS consists of the following three elements:

The physical database:
        The collection of files that contain the data

The database engine:
        The software that makes it possible to access and modify the contents of the database

The database scheme:
        Specification of the logical structure of the data stored in the database