The attributes are your characters primary values - compared to skills & proficiencies, they increase very slowly; unlike the others, luck can't even be trained.
Strength: Strength is primarily useful in combat. It increases your chances of hitting an opponent, and increases the damage you cause if you do hit them; it also determines how big of a weapon you can use. Of course, strength also determines how much weight you can carry.
Dexterity: Dexterity has a number of uses. In combat, it helps you attack more often, attack with enhanced damage, attack with better weapons, and with weapons mastery; it also helps you to dodge, parry, and overall avoid attacks. With high dexterity, you gain more movement points per level, and you regain them quicker when resting or sleeping.
Intelligence: Intelligence enables you to get more out of learning and practicing, and also speeds up gaining skill through the plain usage of the skill; for very high intelligence, it helps you to gain more experience from your kills.
Additionally, intelligence helps you with the spell casting skill, and with high intelligence, you gain more mana per level.
Wisdom: Wisdom is primarily of use in gaining practices; the higher your wisdom, the more practices you gain per level (it does NOT help you gain more trains per level). Besides that, high wisdom lets you gain more mana per level, and improves your dreaming skill.
Constitution: High constitution helps you to gain more HP per level.
Luck: Luck tips random rolls in your favor.