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.)
This article was originally based on material from the Free On-line Dictionary of Computing and is used with under the GFDL.