Affixes are bonuses that roll onto your equipment when it drops, like Rusty or Blessed. The affix shows under the item's name in the color of its tier. Some affixes help and some hurt. Each tier is better than the one before it: Red < Orange < Green < Blue < Pink.
Want a different affix? Oyun, the Mystical's Rerolling Cauldron can reroll it. The Rerolling Guide has the details.
An item has an 85% chance to drop with an affix. Green is the most common tier, while Red and Pink are the rarest. Each tier also changes the item's Item Power.
Event Affixes only roll on their own event items, like Hallowed and Krampus gear.
HATED Affixes only roll for HATED characters (characters with all six totems). The Totem of Avarice also makes Red and Pink affixes more common.
Every affix is made of points. For example, Rusty is -2 Damage. A point is worth more on a low IP item than on a high IP item, so the same affix can give a different number on different items.
On the tooltip, each point shows as a mark next to the number it changes: a + for a bonus, or a - for a drawback. Some affixes mix a bonus with a drawback, but every tier adds up to the same total:
Red: -2 points
Orange: -1 point
Green: +1 point
Blue: +2 points
Pink: +3 points
HATED: +4 points
Event: +5 points
To see an affix's exact numbers on an item, open the item's page and pick the affix from the Affix selector.
An affix only rolls on items that can use all of it. For example, a mana bonus won't roll on a Mask, and an extra projectile won't roll on a weapon that fires a pattern.