"Teaspoon cayenne" refers to a measurement of cayenne pepper, a type of spice. It means using one teaspoon (a small spoon) to add cayenne pepper to a dish or recipe. Full definition
In a bag, mix together flour, 1/2 teaspoon garlic powder, 1/2 teaspoon cayenne pepper, and 1/4 teaspoon salt. (piarecipes.com)
In a pinch, you can make spicy peanut butter by adding 1/2 teaspoon cayenne powder (or more to taste) to 3/4 cup of peanut butter and mixing it well. (fieryfoodscentral.com)
Usually I never put more than 1/4 teaspoon cayenne in a dish or it gets too strong. (greenkitchenstories.com)