Quality is a property of items, which is represented in-game by the color of the item's name and (in most cases) by a title prefixed to the item's name. An item can have only one quality, which is determined when the item is created and remains unchanged, except in rare circumstances.
Here is the list of qualities.
NK gear has 999999 in every stat except movement penalty, which is set to 0, or a positive quantity to increase movement speed.
Strange gear tracks the number of kills you make with said weapon, and you can attach them with strange parts. For armor, it is damage taken. Armors that can inflict damage come with both. Note that this only applies to armors with a natural damage, such as the Titan Teslashock.
Unusual gear pieces have special visual effects on them, like lightning, snow, fire, etc. These can also come in strange.
Decorated gear are simply colored re-skins, but they can also come in strange and unusual.
Vintage gear are "Legacy Weapons", but have had some stat changes and as such all gear affected that were acquired before the patch have been upgraded to Vintage.
Haunted gear are functionally the same to normal gear, but the name is green, and they are boosted during Halloween of during a full moon.
Community gear is awarded to valuable community contributors and bear a special visual effect, just like an unusual, but the only effect for Community gear is the "Community sparkle". They are also shinier in appearance. Those who receive Community gear get automatically 10*** if it is a weapon, 10** if armor.
Self-Made gear is awarded to a community contributor who manages to get his/her submission accepted into the game. He/she then receives a Self-made quality version of his accepted submission, automatically 10*** if it is a weapon, 10** if armor.
Collectors is acquired by trading in 200 copies of the same gear of normal quality, (Acquired from stongboxes, not bought) Though they are functionally identical to normal gear, it can show a player's experience with the game.