A composite key is a database key whose value is made up of multiple typed values
A Composite Key is a Key that is made up of multiple columns
Any column(s) that can guarantee uniqueness is called a candidate key; however a composite key is a special type of candidate key that is only formed by a combination of two or more columns. Sometimes the candidate key is just a single column, and sometimes it's formed by joining multiple columns.
A composite key can be defined as the primary key. This is done using SQL statements at the time of table creation. It means that data in the entire table is defined and indexed on the set of columns defined as the primary key.
Dr E F Codd's Relational Model demands that:
Data is organised into table and columns
Rows (as distinct from records) are unique
A Key is made up from the data (ID, GUID, etc. columns are not data).
In any given table, this naturally leads to multiple columns being used to provide row uniqueness, and to identify each row. That is a composite Key.
Composite Keys are the hallmark of a Relational database (those that conform to Relational Model), without them the database does not comply, and is therefore non-relational.
SQL-compliant platforms provide complete support for composite Keys.
Non-compliant platforms have partial support for composite keys, and usually necessitate single column keys.
Further reading