If both item slots are empty, each unused action point gives you a +2 instead of +1 towards your Armor Class at the end of your turn, plus 1/12 of your unarmed skill.”— Fallout 2 (patched) In-game description
While it states that both item slots must be empty, that is not entirely accurate. It really requires not holding a gun or melee weapon (anything that is visible in the character's hands). This perk will work if wielding unarmed weapons (such as brass knuckles, boxing gloves, power fist), throwables (grenades, rocks), or any non-weapon item.
HtH Evade shares the Vault Boy image with Artful Dodger.
The usefulness of this perk could be debated, as Armor Class is considered the weakest form of defense, compared to Damage Resistance and Damage Threshold. At a respectable Unarmed skill level of 120%, it would only provide 10 extra AC before factoring in any unused AP for an extra 2 AC each. Unfortunately, this will rarely decide if the character is hit by an attack or not, as by Level 12, many enemies will have high enough combat skills that they are almost guaranteed to hit regardless of Armor Class rating. This is compounded by the fact that as a melee-range character, enemies will have no range penalties to hit. Other than for roleplaying reasons or personal preference, this perk will rarely provide any tangible benefit. SPECIAL stats allowing, perks like Toughness and Lifegiver will in almost all cases outperform it.