In the relational model of databases, a primary key is a specific choice of a minimal set of attributes (columns) that uniquely specify a tuple (row) in a relation (table). Informally, a primary key is "which attributes identify a record," and in simple cases constitute a single attribute: a unique ID. More formally, a primary key is a choice of candidate key (a minimal superkey); any other candidate key is an alternate key.
A primary key may consist of real-world observables, in which case it is called a natural key, while an attribute created to function as a key and not used for identification outside the database is called a surrogate key. For example, for a database of people (of a given nationality), time and location of birth could be a natural key. National identification number is another example of an attribute that may be used as a natural key.
In relational database terms, a primary key does not differ in form or function from a key that isn't primary. In practice, various motivations may determine the choice of any one key as primary over another. The designation of a primary key may indicate the "preferred" identifier for data in the table, or that the primary key is to be used for foreign key references from other tables or it may indicate some other technical rather than semantic feature of the table. Some languages and software have special syntax features that can be used to identify a primary key as such (e.g. the PRIMARY KEY constraint in SQL).
The relational model, as expressed through relational calculus and relational algebra, does not distinguish between primary keys and other kinds of keys. Primary keys were added to the SQL standard mainly as a convenience to the application programmer.
Primary keys can be an integer that is incremented, a universally unique identifier (UUID) or can be generated using Hi/Lo algorithm.
Primary keys are defined in the ISO SQL Standard, through the PRIMARY KEY constraint.
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A foreign key is a set of attributes in a table that refers to the primary key of another table. The foreign key links these two tables. Another way to put it: In the context of relational databases, a foreign key is a set of attributes subject to a certain kind of inclusion dependency constraints, specifically a constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S, and furthermore that those attributes must also be a candidate key in S.
In database design, a composite key is a candidate key that consists of two or more attributes (table columns) that together uniquely identify an entity occurrence (table row). A compound key is a composite key for which each attribute that makes up the key is a foreign key in its own right. Composite keys have advantages similar to that of a natural key as it is often composed of multiple natural key attributes.
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