Spellcasting Implements, such as Thaumaturgy staffs, grant an implement bonus to Spell Power, increasing the damage dealt/healed by spells. All weapons that grant any kind of equipment bonus to Spell Power (e.g. Potency or Devotion) also grant implement bonus. Implement bonus increases your universal spell power (all spells), even if the weapon enchantment is not universal (e.g. Combustion).
The implement bonus is equal to 3 * enhancement bonus of the weapon, e.g. a +4 weapon grants a +12 implement bonus to spell power. Effects that increase enhancement bonus of a weapon, e.g. Artificer infusion Enchant Weapons, also properly increases the implement bonus.
Multiple sources of implement bonus do not stack, only the highest applies. However, implement bonus does fully stack with other sources of Spell Power.