To quote that page: DB Offline Errors: Tracks severe errors that cause SQL Server to take the current database offline.
I can't recall that I have ever encountered this situation, or, wait, maybe that was happened on that fateful early Saturday morning many years ago. The customer had a malfunctioninh I/O subsystem that cause corruption galore. At some point it was so bad, that SQL Server decided that it to had to run recovery on the database, and then there was a corruption error during the recovery as well, and this was when SQL Server gave up on that database. Maybe there was a DB Offline error.
As you may realise, this is not entirely easy to simulate.
I should add that the SQL Server version the above happened on was SQL 2000.