In Ubuntu, each folder can have its own filesystem. That means you can move any folder onto its own partition, another disk or even on a remote network. This is particularly popular for home directories, since that means you can reinstall Ubuntu without changing your personal settings or loosing any files. It's also popular in networks where users should be able to log onto different machines and still get their personal settings and files. But it is useful in many different cases, such as yours.
Applications aren't installed into a specific folder, like you seem to suggest. Different parts of the application is placed in different parts of the filesystem. The main program is usually placed in /usr/bin, whereas configuration files are placed in /etc, for instance. In your case, MySQL, the databases themselves are placed somewhere in /var. I think /var/mysql.
Since /usr and /var are both directories in the root filesystem, they will use the root filesystems space. But as I said, you can move them to different filesystems. In the case of MySQL, you can configure where databases are stored. You could easily move databases to /home/username/.mysql/databases for instance.