The log page lists the latest events and can help with both satisfying your curiosity as well as debugging configuration issues or bugs in the plugin.
Major events such as new keywords or backlinks that have been verified will be listed.
With never versions of SEO Booster PRO, you can choose between different levels of debugging.
Default setting is both levels turned off. Major events will still be noted, but not much information.
With Detailed logging
If you wish to have more detailed logging turned on, go to the settings page and turn on detailed logging.