WordPress has support for more then one database type, but primarily uses MySQL as it’s database choice. User information, post data, comments, etc, are all stored in the database.
Plugins and themes by contrast are not stored in the database. these are actual PHP, CSS, JS, HTML, etc, files that are stored on the server. A plugin can create a database table and use the database for storage, but the plugin mechanics and code are stored as files.
It is important to backup your WordPress database in a regular and automatic fashion. If your WordPress database gets corrupted (for any number of reasons) then a significant amount of data can be lost.