A relational database is a database based on the relational model.
Strictly speaking, this means a relational database takes the form of a specific collection of data. The database software that is used to manage the data is called a relational database management system, or RDBMS. (However, common usage doesn't always preserve this distinction.)
Relational databases should be stored in normal form.
This article contains material from relational database at FOLDOC; used with permission.