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An abbreviation for the Structured Query Language (can be pronounced S-Q-L or See-Quel, although the latter is discouraged on the grounds that there is already a programming language called Sequel).
It is the main query language used for relational DBMSs (DataBase Management Systems), but many have their own customised superset/subset of SQL that suits their purposes. For example, MySQL uses the LIMIT clause to return a select number of rows, whereas ANSI SQL specifies the TOP clause. Some databases even use different keywords for their data types, such as Oracle's VARCHAR2.
SQL is one of the few 4th generation 'programming languages'. It's clever because you tell it what to do, not _how_ to do it.