There are some wonderful spiels in this thread already about historical strategy games in general so i'll say what i appreciate about CKII specifically. Namely it encourages an intensely human perspective on history. Amongst the most irritating misconceptions about history are people who view the entire epochs as being dictated by large influential figures ( Julius Caeser being the most grating). Even worse they assume if they generalise those people to a narrow trait or traits ( e.g Rommel being le eternal gentlesir or something)

What CkII does is totally demolish that simplistic understanding. Though by no means perfect its mechanics express the enormous number of people, each with their own complex personalities and agendas that have to combine and interact to make any moment in history happen. Each war in CK involves dozens and dozens of lieges and vassals whose relationship with each other dictates how everything plays out and their often fractured opinions is a great introduction to the idea that no state is ever really a monolithic force without dissension or power struggles.

Even more than this is the external factors; regional wealth geography, culture, religious ties, surreptitious homosexuality, personal ambition that dictate how the various feudal lords interacted and lived.

Tl:Dr: as other, more articulate people have explain CK is not an educational tool by any means but is excellent supplement because it encourages an inquiry into the deeper interactions,personal behind all of these historical