There is no kind of food known as "Cheddar." Cheddar is a village in the Somerset region of England where the cheese now known as Cheddar cheese was first made in the sixteenth century and which came to be named after the town.

The excited promotional copy doesn't say "MADE WITH REAL CHEDDAR CHEESE!" - it says "MADE WITH REAL CHEDDAR!" Knowing what I do of the relation between advertising and the truth, I can only assume that a small bit of the village of Cheddar - 10 mg of dirt or so from the hill behind City Hall, perhaps - is sprinkled among the contents of every box of crackers.