Certain enemies are weak to certain things. Unlike Combat Weaknesses, Special Weaknesses increase the amount of damage done to an enemy. They are typically designated as having a percentage weakness to a type of damage. For example, you strike a werewolf with an unblessed silver weapon and deal 10 damage. Werewolves are 25% weak to silver, so the hit would be 12.5 (10 x 1.25), rounded down to 12.
Silver has a slightly divine property of being able to hold blessings extremely well. This property on its own gives it a slight advantage to fighting unholy beings even if it is unblessed.
Spells, prayers, and weapons can be blessed by the gods and do damage to certain unholy entities. The weapons are usually made of silver and are blessed by Guthix, Armadyl, Saradomin, or Seren.
Some rare or unique weapons and materials do immense damage to certain creatures. Obtaining these weapons and materials are huge ordeals in-and-of themselves and are rewarded with wonderful damage bonuses.
Note that Special and Unique weaknesses do not stack for the same enemy. If a blessed silver weapon has a Blisterwood handle, it does 100% more damage to Vampyres, not 150%. However that same weapon will do 100% more damage to Undead as usual.
Vampyres take 100% more damage from Blisterwood weapons and cannot predict these attacks.
Undead take 150% more damage from characters wearing Salve Crystal necklaces.
Undead take a staggering 200% more damage from characters wearing Enchanted Salve Crystal necklaces.