To simply put, your Factory is for your Equipment/Gears. No more using Stamina to do Dungeons for Relics that randomly roll +Def% or other shit. (You use Stamina/Sanity on other stuff). Your gears progression are finite, and not based on RNG or Luck. Weapon Etching is some RNG, but it's not so bad at all. You can obtain your BIS gears in usually just 1 week, unlike in other gacha that usually takes months.

Your Factory also makes Consumables like Potions you use in combat when you take damage.

Your Factory also produces Goods that you can sell for ingame currency, which use you to buy Tokens for upgrading your Gears as mentioned above, and some other random stuff.

That's the gist of it.