MySQL
MySQL is the best free and most popular open-source relational database management system. It is very powerful RDMS and it offers many features. To access databases, insert data, create tables and other SQL (Structured Query Language) is used. This is the most popular language when it comes to databases. MySQL is platform-independent and can run on many operating systems including linux, *bsd systems, windows, mac, novell netware and lots of others. To developers mysql offers api functions available in several programming languages, with which the developer can communicate with MySQL server and perform queries. When you talk about MySQL, you can not not mention PHP, mostly because of the popularity of the web applications (wordpress, drupal, joomla and million other applications that can create almost any type of website.). As a fact is that wordpress, drupal, joomla and other scripts are installed on millions of websites worldwide, and popular sites use MySQL and PHP including facebook.com, google, wikipedia and many others. Currently MySQL is owned by Oracle corporation. Several tools have spawned to manage MySQL most notably phpmyadmin tool.
Justhost and MySQL
MySQL runs great on Justhost. You can create unlimited databases and database users (with permissions) via cPanel tool and manage with phpmyadmin. Remote MySQL is allowed. This wordpress blog is the best test Justhost MySQL, and the results are excellent(fast queries, all features available etc.).