Relational databases are databases system designed based on the relational database model. In a relational database model, data are stored in a relation or table (those terms may be used interchangeably.) Each table contains rows or records, (also called tuples), and columns which represent attributes or fields. Each record or row is represented by a unique field known as the Primary key.
In the context of relational databases, a foreign key is a referential constraint between two tables. The foreign key identifies a column or a set of columns in one (referencing) table that refers to a column or set of columns in another (referenced) table. The referenced columns must be the primary key or other candidate key in the referenced table.
The values in one row of the referencing columns must occur in a single row in the referenced table. Thus, a row in the referencing table cannot contain values that don't exist in the referenced table (except potentially NULL). This way references can be made to link information together and it is an essential part of database normalization.
Multiple rows in the referencing table may refer to the same row in the referenced table. Most of the time, it reflects the one (master table, or referenced table) to many (child table, or referencing table) relationship.
The referencing and referenced table may be the same table, i.e. the foreign key refers back to the same table. Such a foreign key is known in as a self-referencing or recursive foreign key.
A table may have multiple foreign keys, and each foreign key can have a different referenced table. Each foreign key is enforced independently by the database system. Therefore, cascading relationships between tables can be established using foreign keys.
Improper foreign key/primary key relationships or not enforcing those relationships are often the source of many database and data modeling problems.