SQL (Structured Query Language) is a language used to communicate with a database.MySQL is a particular flavour of SQL, which supports a slightly different set of commands to other database types (while still having a lot of similarities, and some commands in common).
Despite the name, it's more than just a "query language": it is actually the entire database system. Rather than comparing this to a hard drive, it can perhaps more accurately be compared to an Excel spreadsheet. In a spreadsheet, you have a bunch of 'worksheets' which are your 'database tables', columns (A-Z and beyond) which are your database columns or fields, and rows (1 to around 65000) which are your database rows or records.
Whereas with a spreadsheet you can just look at it and find what you like, there needs to be some structured way to do this with a database so a program can specifically query just the information it needs. An SQL query could retrieve all the records in a table, or it could retrieve just a few based on the value of certain fields (eg. retrieving just the value of the email_address field of a particular user based on the username or user_id provided).