Here is what each stat does.
Strength: Stat which increases the attack strength and the maximum weight of a character.
Agility: Stat which affects the attack speed and dodge rate of a character.
Vitality: Stat which increases a character's maximum HP amount, as well as decreases the amount of damage inflicted by enemies. Also reduces duration of abnormal status.
Intelligence: Stat which determines a character's maximum SP amount, Magic attack strength and Magical defense.
Dexterity: Stat which increases a character's attack accuracy and maximum weapon damage. Also affects on skill casting time.
Luck: 3 points of Luck increases critical rate by 1%, and 10 points increase the chance of perfect dodge by 1.