Humans are unable to digest cellulose because they do not have necessary enzymes required for cellulose digestion, nor do they have symbiotic bacteria to perform the digestion for them; they can digest starch because they have the required enzymes to break it down. The linkages in the molecules dictate its digestibility.
Cellulose is composed of a chain of linear polysaccharide polymers and glucose monosaccharides. They are arranged in a beta acetal linkage that require specific enzymes for digestion. Humans do not have enzymes that are capable of breaking the beta acetal linkage, causing the cellulose to pass through the digestive system in tact.
Starch is made of glucose molecules arranged in an alpha acetal linkage. Enzymes in the human stomach are capable of breaking this linkage.