A database is an aggregation of data of various types, in which the relations between the data items are made explicit. It can be best thought as a collection of tables, each representative of a relation between data.
For example, a firm might consider relevant to some purpose the following employee personal data, for all its employes: first name, last name, social security id., office number, phone number, date hired. This very list defines by itself a relation between data sets, each being a collection of possible values for each data item (i.e. the set of last names, the set of phone numbers, etc.). This relation can be made explicit in tabular form by listing the elements of the relation itself (i.e. the elements of the cartesian product set), e.g.
For permanent storage purposes, the data need will be stored in data files on a storage media. A data file will often represent a particular relation defined on the data of interest.
The elements of a relation (the ``rows'' of a table) are in general aggregates of data of different types (numbers, names, various alphanumeric codes). They are referred to as records in data reresentation terminology, while their components (the elements of a row) are called fields.
A database system (DBMS) is a complex software programs that controls the organisation, storage and retrieval of data (fields, records and files) in a database. It also controls the security and integrity of the database. The DBMS accepts requests for data from the application program and instructs the operating system to transfer the appropriate data.
When a DBMS is used, information systems can be changed much more easily as the organisation's information requirements change. New categories of data can be added to the database without disruption to the existing system.