Specialization in the weapon style teaches you to expertly wield the weapon. This further training gives you the knowledge that is required to become a master with the weapon. Weapons masters are able to "move faster than the eye can follow" and frequently get added attacks per round with the same weapon. Only certain classes can specialize in certain weapons, some are unable to go past general proficiency.
Specialization in each of the weapon styles (pierce, blunt, slash, ranged) can only be done AFTER you have become very proficient (combat discipline) in the weapon.