Armor and rings can have traits: extra bonuses like taking less projectile damage or resisting Slowed. They're listed under Traits: on the item's tooltip.
Traits have ranks from I to V. Getting the same trait more than once raises its rank, like Slowed Resistance II.
An item gets its first trait at 15 Item Power, and another every 10 IP after that:
A good affix or quality can push an item over the line and give it an extra trait. A bad affix can take one away. See Item Power.
An item can have up to 3 different traits, and a trait can't go past rank V.
Armor and rings roll from different lists. Each rank adds the amount shown again.
Resistances: A debuff from an enemy hits you one level weaker per rank. A debuff from your own gear has a 20% chance per rank not to hit you at all.
Proliferation: Only rolls for a stat the item already gives.
Conversion: Turns part of one stat into another, like WIS/DEX Conversion. It can only move stats the item already has.
Proc traits: Only roll on items that have a proc.
Some items always come with a certain trait. These are called pinned traits, and they can't be rerolled.
Every other trait can be rerolled at Oyun's Rerolling Cauldron. Each rank is rerolled on its own, so you can change one rank of a trait and keep the rest. See the Rerolling Guide.