Strikest, when you get past the Goddesses (Deis, Troy, Seso, and Life) there's a "World Power" thing. When you kill that, you enter the Chaotic World. This is where Proficiencies come in, because most items have different stats based on if you are proficient with that weapon/armor. If you aren't proficient in it, it'll be weaker than for someone who is proficient with it. Almost all effects are nerfed when you aren't proficient with it compared to someone who is proficient with it.
What happens to them: Weapons lose damage, stats too (if applicable), and perhaps abilities (depending on the weapon). Armor also may lose abilities (not seen one with an ability myself), Heavy Plate I think slows you down more (well, it should), it gives less armor, also less regen/stats (if applicable), and if it's a Chain armor, it'll lose some of the evasion %.