The section labeled "Old materials that are only used to make low iLvl items" can be a helpful tool for getting rid of materials that you may have stocked up, but that aren't used in any high ilvl crafts.
You can input a value in the "Min Resulting iLvl" filter to tell the optimizer that you want to keep all the materials that are used for making items with a resulting item level equal to or greater than this value.
This optimizer DOES span entire recipe trees to find what a material can be used for, below will be a couple of examples. These examples use information accurate as of patch 5.2.
Our first example will be Gold Ore. Directly, it can only be used to craft 5 items (Aurum Regis Nugget, Gold Ingot, Rose Gold Nugget, Stonegold Ingot and Stonegold Nugget). Of these, Stonegold Ingot has the highest item level at 395. However, through the use of Stonegold nuggets, we can make several weapons that are item level 450, such as Skystrider and Tutelary, among many others. Therefore, gold ore is treated has being useful for crafting items up to ilvl 450, and if your filter is set to anything equal to or below 450, gold ore will NOT appear in the list (remember, the optimizer is telling you things you should be able to discard). Conversely, if your filter is set higher than 450, gold ore will be listed, indicating it cannot satisfy your ilvl requirement and CAN be discarded (barring specific uses you may have for it).
Our second example will be Tin Ore. Directly, it is only used to craft a Bronze Ingot, with an item level of 1. However, we all know Bronze Ingots are used to make several items with a higher item level than that, and so the recipe tree is scoured to see what it can make. Tin ore is a strange beast in this regard; it can be used to craft the Order of Nald'thal Lectern, a housing item with an item level of 110. So in the midst of gear around item level 20-30 that bronze is used for, this one furnishing bumps it up to ilvl 110 for filters. Further, bronze is also used for several Company Workshop crafts, including airship and submarine parts. These are crafts that are pretty specific to each individual, and it is up to the user to decide if they want something like tin ore sitting around (in this case though, tin ore can be bought from several vendors for 2 gil each, so you may want to take that into account).
Regardless, tin ore will only appear if your ilvl filter is higher than 110 for this reason, if you have something you personally want to keep it for, simply click the eye on the right side to hide it from view, same as the other optimizers.
All in all, this optimizer can be good for clearing out the troves of low level crafting materials you may have been holding on to (loads of mushrooms and branches from early leveling anyone?) and not sure if they were going to be used for higher level crafts. It is, however, not an end-all to what you should and shouldn't keep, and a bit of discretion will go a long way while using this particular tool.