Artyom Shalkhakov wrote

I would say that it [iteratee] just tells us how to react to various forms of input. :) This is much like the function you pass to foldr.

Precisely. To sum up all elements of Data.Map, we do Map.fold (+) 0 mp to sum up all elements of a set we do Set.fold (+) 0 st ditto for any other foldable data structure. Clearly the function that sums the current element with the accumulator, (+), doesn't know or care from which collection the elements are coming from. The initial seed, 0, is again unaware of the collection. Iteratee is indeed the function that you pass to fold (combined with the seed for practical reasons). One may conceptually consider iteratee to be a pair of the function to feed to fold, and the initial seed (the accumulator in the above example). That achieves the separation of concerns: fold (aka, enumerator) has the intimate knowledge of the collection and how to get to the next element; iteratee knows what to do with the current element.