When making a sugar-based candy, any foreign ingredients like fat, acid-like vinegar or corn syrup help keep it smooth and from re-developing crystals. This is a smooth candy so it has all three. Taffy started in 1885 at Fralinger's on the Boardwalk in Atlantic City, N.J. The story goes that one day large waves came up and drenched all the product in the store, coating it with salt water. The next day when it was tasted they changed the name to "Salt Water Taffy." It became popular to have social events called Taffy Pulls to allow young men and women to get together and be close but not too close. Interesting old terms: crystallizing was called "graining" or "cause the candy to sugar."
Put all the ingredients in a large saucepan and gently stir them to combine. Place a candy thermometer on the side of the pan and bring to a boil, stirring only to prevent burning. Cook to the "firm ball" or "hard ball" stage (255 degrees F), and remove from the heat. Stir in the extracts and pour onto a silicone baking mat-lined sheet pan. Let it cool enough to handle then start rolling it into a log and stretching or pulling the taffy to work air in, and make it white and opaque. Keep pulling and twisting until it hardens. You'll finish with long ropes of taffy. Cut it into pieces or shape into figures and animals.
Some tips when making taffy:
Oil the top 1-inch of the saucepans wall to keep the sugar from boiling over.
Always use a pan bigger than you think you need to prevent boiling over.
Always use a burner as big or bigger than your pans bottom.
Never scrape the bottom of the pan at the end, just pour out the syrup.
Wash down the sides of the pan with a clean wet pastry brush to avoid crystallization.