You'll need to choose which of your computers, Kodi devices, or NAS will be the MySQL server. The server needs to be on 24/7 or have wake-on-lan (preferably the former), and needs to have a local static IP. You will probably want the Kodi device that is hosting most or all of your videos and music to also be the MySQL server, but this is not required.
Please Note: Don't create the MySQL databases on your server. Simply set up the MySQL server itself, as Kodi will create the specific databases by itself.
Also: Some versions of MySQL set their passwords to expire by default, even the root password! If the password expires, Kodi cannot access the database and the TV Series and Movies libraries will disappear.
To avoid this and/or fix it after it happens, make sure the account's password does not expire. (See: https://dev.mysql.com/doc/refman/5.7/en/password-management.html )
MySQL can be installed on just about every major OS:
Important: Please use only supported versions of the MySQL or MariaDB server. As of January 2019, this is MySQL in at least version 5.6 or MariaDB in at least version 5.5.