The idea

If a derived table cannot be merged into its parent SELECT, it will be materialized in a temporary table, and then parent select will treat it as a regular base table.

Before MariaDB 5.3/MySQL 5.6, the temporary table would never have any indexes, and the only way to read records from it would be a full table scan. Starting from the mentioned versions of the server, the optimizer has an option to create an index and use it for joins with other tables.

Example

Consider a query: we want to find countries in Europe, that have more than one million people living in cities. This is accomplished with this query:

select * 
from
   Country, 
   (select 
       sum(City.Population) as urban_population, 
       City.Country 
    from City 
    group by City.Country 
    having 
    urban_population > 1*1000*1000
   ) as cities_in_country
where 
  Country.Code=cities_in_country.Country and Country.Continent='Europe';

The EXPLAIN output for it will show:

+----+-------------+------------+------+-------------------+-----------+---------+--------------------+------+---------------------------------+
| id | select_type | table      | type | possible_keys     | key       | key_len | ref                | rows | Extra                           |
+----+-------------+------------+------+-------------------+-----------+---------+--------------------+------+---------------------------------+
|  1 | PRIMARY     | Country    | ref  | PRIMARY,continent | continent | 17      | const              |   60 | Using index condition           |
|  1 | PRIMARY     | <derived2> | ref  | key0              | key0      | 3       | world.Country.Code |   17 |                                 |
|  2 | DERIVED     | City       | ALL  | NULL              | NULL      | NULL    | NULL               | 4079 | Using temporary; Using filesort |
+----+-------------+------------+------+-------------------+-----------+---------+--------------------+------+---------------------------------+

One can see here that

• table <derived2> is accessed through key0.
• ref column shows world.Country.Code
• if we look that up in the original query, we find the equality that was used to construct ref access: Country.Code=cities_in_country.Country.

Factsheet

• The idea of "derived table with key" optimization is to let the materialized derived table have one key which is used for joins with other tables.
• The optimization is applied then the derived table could not be merged into its parent SELECT
  • which happens when the derived table doesn't meet criteria for mergeable VIEW
• The optimization is ON by default, it can be switched off like so:

set optimizer_switch='derived_with_keys=off'

See also

• Optimizing Subqueries in the FROM Clause in MySQL 5.6 manual
• What is MariaDB 5.3
• Subquery Optimizations Map