Dodge is one of the three avoidance mechanics in the game. Dodge Rating, usually expressed as a percentage, is your chance to dodge an incoming melee attack (do not confuse Dodging with Missing - they're unrelated). When a player dodges an incoming attack, the entire attack is avoided. Players cannot dodge attacks coming from behind them, but mobs can. Additionally, a player cannot dodge if they are stunned. Dodge percentages are derived from three things: Defense Skill, Dodge Rating, and Agility. As mentioned above, 1 Defense skill gives a 0.04% chance to dodge an attack, and the dodge derived from Agility is purely dependent on class, spec, and level.
Dodge is a complex mechanic because it is subject to diminishing returns. This means that the higher your dodge chance gets, the more points of Dodge Rating you'll need to increase it further. That said, there are two kinds of Dodge - Diminished, and Undiminished. Undiminished Dodge doesn't trigger Diminishing Returns, and is therefore preferable. Undiminished Dodge is dodge from your class' base dodge chance, dodge from Talents (like Anticipation), and Dodge Derived from your base Agility. Dodge from Dodge Rating, Dodge derived from Agility from gear and buffs, and Dodge derived from Defense is all subject to Diminishing Returns.
Dodge is found on red gems.