I increased the quality of my weapon by 20% but I don’t notice any improvement in my weapon?
The DPS should have increased. Also, quality kicks in when you put new affixes.
for weapons, Item Quality affects the Weapon Damage. Items found as treasure or bought with Dust or Gold can have an Item Quality of up to +/- 10%.
((base weapon damage + power stat) x ((1 + item quality) x (1 + weapon damage%)) + weapon damage+) x (1 + elemental damage%) + elemental damage+ = Weapon Damage
for the other 4 Items, Item Quality affects the Items Armor.
for all Items, higher Item Quality affects the chances of affixes being/becoming max value for the items level.
for Pets, Emeralds don’t work on them, but I think Item Quality affects how fast affixes are improved when they level up and when the Pets Rescued Feat is finished.
Welcome to DQ Forums @Kawaki !
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Maxing out quality is the very first thing that should be done when crafting a new item.
“Why can’t I get a decent stat roll?” 
“Oh no, my quality is minus 9!” 
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