Quote Originally Posted by Brave_Sir_Robin
A civil war is triggered when a number of the factions generals have low loyalty. If there are enough low loyalty generals, they will split away from the faction becoming rebels. This usually happens when the faction leader has low influence or if the leader has just died and a weaker king has taken the throne. Civil wars vary in size depending on how many generals rebel against the crown.
A quick addendum: A civil war can also occur if your faction leader dies without a direct heir (i.e., he has no sons or brothers over the age of 16), but has two (or more) "royal generals" running around the kingdom -- this represents multiple claimants trying to sieze the now-vacant throne. Good times for everyone.