Health is your green bar. While every character wants to avoid death, Health is especially important to Tanks.
Power is your blue bar. No Fighting Style provides any bonus to Power.
Might adds to the damage of your powers; that is, the 6 abilities you have in your loadout. It's most important for DPS characters.
Precision adds to the damage of your Fighting Style attacks. No Fighting Style provides any bonus to Precision.
Defense reduces the damage you take from NPCs. It is mostly important to Tanks.
Toughness reduces the damage you take from other players. It is important to those who focus on PvP. The bonuses to Defense & Toughness provided by Fighting Styles always come together; any Style which buffs Defense also buffs Toughness by the same amount.
Dominance determines the duration of your crowd control powers, such as stuns and confuses, on targets. Various endgame Raids and Alerts have recommended Dominance levels. This is required for Controllers.
Restoration affects your Healing powers. The higher your Restoration, the more you heal. Obviously it is important for Healers, but it is also key to Fire Tanks who use self-heals.
Vitalization affects your ability to restore the blue bar (Power). In DCUO, the ability to "heal power" is a Controller function, so Vitalization is mostly important to Controllers.
Critical Attack Chance and Damage is not listed on your stats and there is no way to really monitor it in battle. Presumably it increases the percentage chance of a critical hit, and increases your critical attack damage by a flat percentage as well. It is mostly important to DPS characters.
Critical Healing Chance and Effect is also not listed on your stats and there is no way to track it. Presumably it affects powers which you activate, whether they target you or someone else. Critical Healing Chance and Effect is important to Healers and to Fire-Tanks.
Stealth Rating affects your ability to go unseen when using Stealth/Hide, Disguise, or Canine Form (available in the Gadgets, Mental,or Shapeshifting trees, respectively). This stat is not tracked anywhere you can monitor, but is only important if you have a power which lets you enter Stealth.
