Ilvl determines how much stats you can put on a single piece of gear. For example, let's say an ilvl 50 hat has budget 30 item points allocate stats with, and let's say every one point of Strength, Vitality, etc. cost 1 item point to put in the gear and every one point of secondary stats cost 2 item points to put in. You then use that to put stats in the gear without going over the cap.

That would be a rough example how ilvl works. Different items will have different stat caps on them even if they are the same ilvl, like how in FFXIV chest and leg pieces have more stats than hands. Ilvl will also probably always exist, regardless if you can see it or not.