A food hyper sensitivity, is a form of reaction that involves an immune reaction to an allergen BUT, unlike a food allergy, it does not involve the IgE antibody.
It is important to note that food hyper sensitvitiy is different from food allergy however the diagnosis and need to avoid the allergen make it very similar.
Non-IgE hypersensitivity reactions are generally not immediate, instead the symptoms develop over several hours to days after ingestion of an offending food. Reactions do not manifest with itching, hives, swelling, coughing or wheezing, etc, typically only involving the gastrointestinal system, and other body organs are not involved.
Coeliac Disease is a well known example of a food hyper sensitivity, with Infantile Colic (baby colic) also often blamed on a hyper sensitivity to milk.