THIS IS 2.0 INFORMATION AND MOSTLY STILL VALID FOR 3.0 BUT THERE WILL BE UPDATES.

Strength: Increases melee attack power and the percentage of damage mitigated by block and parry.
Dexterity: Increases ranged attack power and the chance of blocking or parrying an attack.
Vitality: Increases maximum HP.
Intelligence: Increases attack magic potency.
Mind: Increases healing magic potency.
Piety: Increases maximum MP.

It is suggested to allocate your attribute points like this:
Gladiator / Paladin: VIT > STR > DEX
Lancer / Dragoon: STR > VIT > DEX
Marauder / Warrior: VIT > STR > DEX
Pugilist / Monk: STR > VIT > DEX
Archer / Bard: DEX > PIE > VIT
Thaumaturge / Black Mage: INT > PIE > VIT
Conjurer / White Mage: MND > PIE> VIT
Arcanist / Scholar: MND > PIE> VIT
Arcanist / Summoner: INT > PIE > VIT

For more information you can refer to the Primary stats for each class thread.