Dodge is a status which makes it so that the affected fighter will dodge the next attack. This includes attacks that inflict a status ailment and don't directly damage the fighter, like Slime Ball.
The effect lasts until an attack is successfully dodged or the Dodge user's next turn begins.
In the Parallel Universe episodes, Dodge is changed to Dodge?. This status is identical, except that the dodge has a 50% chance of occurring instead of a 100% chance. It lasts until an attack is successfully dodged or until the Dodge? user's next turn begins.
Neither version of Dodge will prevent damage from gadgets, Jackpot bonuses, or Witch's Throw Dice ability.