The simplest definition of "organic matter" that I have found in the public forum is "an item of decaying plant or animal material". This opens up the definition to include anything made from animals, or plants (living items) - clothes, wooden items, food items that are plant based or animal based. TSOs should be able to relate that to someone that asks them (at least, in my experience, the vast majority of them have been able to). The same goes for inorganic materials - inorganic is simply defined as things that are not derived from living organisms (if we get a bit more technical, I believe a more precise definition is material that lacks carbon that was organically produced - although, I am not a Scientist). Most TSOs will be able to articulate the differences to a passenger. YMMV (I know, I know!), but I have heard tons of TSOs at a few airports explain this quite well.