It's use is governed by which license you received it under. If you received it under the GPL then your uses are limited by the GPL.
With the GPL you can use a database in a commercial web site all day long and owe no one nothing.
However, if you build a system with a GPL'd product in it, you must provide the source code of all the GPL'd code, and all the new code you wrote that is encumbered by the GPL products on the machine (there may or may not be encumberances, depending on how they interact etc...)
If you want, you can get a commercial license from MySQL that will let you sell a product with MySQL in it and it will not be GPL encumbered by MySQL, since in that form it will be commercially licensed. But you have to pay MySQL for that.
So, for a commercial website, using the GPL version of the MySQL database should be a zero cost option, as you aren't reselling the database.
Way back when there was a weird Linux is free windows costs money license, but I don't think they have that license anymore because it isn't GPL compatible.