On weapons, it adds increased damage of that (singular) element, with the effect being stronger the more +'s there are.
On armours, it adds an amount of resistance to that element based on the number of +'s; the value listed in the status menu is effectively the percentage of damage resisted for each element, with some exceptions.
For singular element+ effects, the amount of percentile damage reduced of that element is:
+ = 10
++ = 20
+++ = 25
For the effects of "All Elements+", however, they are always applued to resistance, even on weapons, the amount of which is 5 to each attribute per +.
The exception to the rule of 100 resistance being total immunity to those attributes is that, in the DLC, there are some enemies that use elemental attacks that will still hurt you even with 100 resistance in that attribute, but can be nullified still if you can get 200+ resistance for the element in question. I have previously called these sorts of attack "200% elemental attacks", seeing as you need 200 or more in the resistance to nullify them.
Of note, I have found that the following enemies are capable of using 200% elemental attacks (those attacks that are not nulled by having only 100 resistance, but are nulled by having 200+ resistance):
- Ancient Napdragon - Fire [the forward lunge's shockwave]
- Typhoon Bird - Wind [hitting its wings when it shoots tornadoes forward]
- Fortoise - Fire [×2 attacks]
- Wicked Jaws - Water [the dash attack]
- Legendary Bandit - Earth [the rock avalanche attack]
- Killertaur - Fire [×2 attacks]
- Blazilion/Aqualion/Gustilion - Fire/Water/Wind (respectively, their dash attacks)
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