When changing the status of an application, from the admin panel or from the site, a status change log is written to the database. This always happens, regardless of whether the application status log plugin is enabled.
The plugin opens a page in the admin panel where you can view application status logs. The page is available in the "Applications" - "Application status log" section.
By default, the log is stored for the last 20 days. You can change the number of days to any in the logging settings, but the minimum log is stored for 5 days.