Cellulose is an anti-caking agent used in a wide range of food products, including salad dressings, ice cream and shredded cheese. Its function in shredded cheese is to prevent the bits from sticking together in clumps.
There has been some controversy about the use of cellulose in food. It was approved by the United States Food and Drug Administration despite the fact that it cannot be digested by any vertebrates, including humans.
More traditionally, the substance has been used in wood, paper, cotton, linen, rayon, explosives, as nitrocellulose, and film, as cellulose acetate. However, it is a natural fiber that aids in the healthy functioning of the intestinal tract.
Scare stories "exposing" the use of "wood pulp" in ice cream largely failed to mention this. In fact, cellulose can come from any plant source, including the vegetables we eat, and is perfectly safe.