There are currently four Quality tiers in the game, with four higher ones viewable in the market but unimplemented. They are, in order from lowest to highest, Poor, Basic, Standard, Refined, Epic, Legendary, Artifact and Relic, possibly being part of the game's namesake.
Qualities apply to every piece of armor and weapon, but not (currently) to anything else. Drop rate, attack/defense stat and stat bonuses seem to be tied to Quality tier (see table below). In addition to this, higher tiers generally have better 'materials' that the item is made out of e.g. Wood, Opal etc.
|Tier||Name||Bonus Stats Range|