How much did medieval peasants know about the world?

If by “about the world” you mean about geography, probably very little outside of their immediate area, which they would know in intimate detail. 

First, most people (especially among the peasantry) did not travel or migrate more than a few miles from their place of birth, so the odds of improving your knowledge base by personal experience was low. 

Second, given that basic literacy and education services (or books and other written matter) were pretty rare in this period, having access to geography classes or maps would have been very difficult for peasants.