A schema is a database, so the SCHEMATA table provides information about databases.
mysql> desc INFORMATION_SCHEMA.SCHEMATA;
+----------------------------+--------------+------+-----+---------+-------+
| Field | Type | Null | Key | Default | Extra |
+----------------------------+--------------+------+-----+---------+-------+
| CATALOG_NAME | varchar(512) | YES | | NULL | |
| SCHEMA_NAME | varchar(64) | NO | | | |
| DEFAULT_CHARACTER_SET_NAME | varchar(64) | NO | | | |
| DEFAULT_COLLATION_NAME | varchar(64) | NO | | | |
| SQL_PATH | varchar(512) | YES | | NULL | |
+----------------------------+--------------+------+-----+---------+-------+
5 rows in set (0.00 sec)
The following statements are equivalent:
SELECT SCHEMA_NAME AS `Database`
FROM INFORMATION_SCHEMA.SCHEMATA
[WHERE SCHEMA_NAME LIKE 'wild']
SHOW DATABASES
[LIKE 'wild']