> What exactly is he referring to?
He's most probably referring to the events in Russian history when Russia was on a brink of ceasing to exist as a state. There were a number of grave moments throughout the centuries, to name a few:
1. Mongol invasion of Kievan Rus (XIII-XV centuries)
2. Смутное Время ("Time of Troubles", _as Wiki puts it_ ) (late XVI - early XVII)
3. The Patriotic War of 1812, Napoleon's invasion \- which is, obviously, the closest one to the time "The Brothers Karamazov" is set.