From Diablo 3's Game Guide:
- Strength: The primary attribute for Barbarians. Strength increases Barbarian damage, and increases Armor for all classes.
- Dexterity: The primary attribute for Demon Hunters and Monks. Dexterity increases Demon Hunter and Monk damage, and increases Dodge Chance for all classes.
- Intelligence: The primary attribute for Witch Doctors and Wizards. Intelligence increases Witch Doctor and Wizard damage, and increases resistances for all classes.
- Vitality: Increases Life, the amount of damage you can take before dying.
- Armor: Decreases the amount of damage you take from enemy attacks.
- Damage: Indicates the average amount of damage you deal with your attacks. Damage is derived from your equipped weapons, primary attribute, attack speed, and critical hit chance.
Primary class abilities provide an additional 1% damage per point.
Strength gives 1 point of armor per each point.
Every point of Intelligence grants .1 to all resistances.
As for knowing at a glance what items will be doing by adding stats, you can check the tool tip when comparing an item to what you have equipped, and it will show exact changes to all of your abilities, from damage to protection to health. Positive changes will be shown in green, and negative changes in red.