The Cheese is an item found in Fatty Bear's Birthday Surprise.
Fatty Bear's Birthday Surprise
Fatty Bear will need the cheese in order to gain the key to the attic (it is optional to obtain it, but you will need it if the puppy took the chocolate chips from Fatty Bear) as the mouse that has the key will run away with it as soon as Fatty Bear will try to take the key from it. After Fatty Bear obtains the cheese, he will give the cheese to the mouse in order to prevent it from taking the key away. After that, Fatty Bear will take the key and he can use it to unlock the attic door.
Later Sam plays the game with Darkness after he learns Darkness is not at all what he thought he was.
Russian Blue steals the famous Limburger Cheese from a museum at the start of the game and SPY Fox must go after her in order to get it back. Throughout the levels, SPY Fox can obtain pieces of cheese for points. Only good cheese gives points, bad cheese will decrease points. Eventually SPY Fox manages to arrest Russian Blue and return the Limburger Cheese back to the museum.