Doubles production speed of Statue of Zeus.
Ivory is a hybrid resource. It has some strategic resource-like function by speeding up the Statue of Zeus and allowing the highly-powerful War Elephant, but also luxury-like function with the happiness it provides and the potential further boost with a Market.
War Elephants are more powerful than most units for their time, but require rare Ivory. Unlike Copper and Iron, though, you can see Ivory right from the start of the game, and it can very much be worth getting some just for those War Elephants.