In WordPress, the database version is a number that increases every time changes are made to the way WordPress organizes the data in its database. It is not the same as the version of the database software, MySQL.
For example, the database version in WordPress 3.3 was 19470, and the database version in WordPress 3.3.1 did not change. This tells anyone planning to use backed-up data from the older version that they do not need to check for changes in the structure of the data.
WordPress stores its database version in the database, as the option named "db_version" in every WordPress site's "wp_options" table. (The table name prefix "wp_" may be missing or different in some cases.)