Traditionally, chaff referred to the discarded stems of a cereal crop when it was threshed for the grain. This chaff was very low in nutrients for animals, basically just being straw. For this reason the term "separating the wheat from the chaff" referred to finding taking worthwhile objects/things out of less worthy things.

What is Oaten/Cereal Chaff?
Perrys Chaff is a mixture of oaten and wheaten hay. We cut predominately oaten hay, but also grow wheaten hay as a rotation crop due to the ability to treat oat related weeds in the paddocks. Wild Oats have a similar growing pattern and structure to chaffing Oats. They have a very low nutrient value, and multiply at a significant rate unless treated. Growing a Wheat crop allows us to eliminate wild oats from the paddocks they are in so that the next oat crop grown is cleaner and therefore the chaff is.