Faith governs the Miracle Power and also increases the Magic Defense. It also controls the player's attack power for weapons that scale with Faith, any weapon that are upgraded down the Divine Upgrade or Occult Upgrade paths. Most miracles damage are also increased with faith.
Miracles require a minimum Faith level to cast.
(You can acquire without the required stats and even attune the spell, but attempting to cast will leave your character scratching their head, literally.)
NOTE: Some weapons (e.g. Astora's Straight Sword) require a minimum Faith level to be wielded properly.
If you do not meet the minimum Faith required, you will stagger after every hit on an opponent.
List of weapons and their Scaling
Also see weapon scaling.
Scaling - A
Scaling - D
Scaling - C