A Food Intolerance is generally defined as an adverse, but non-acute and delayed reaction to a food or food component. Wikipedia has a great entry on Food Intolerance. It is different from a Food Allergy, which has an acute and rapid onset caused by an immediate immune response to an allergen.
Food intolerances can have many different causes, but a common cause may be linked to the types of bacteria that are found in the gut. In many cases, providing (sometimes harmful) resident gut bacteria with certain sugars or other compounds that they feed on can cause growth of these harmful bacteria, increasing the levels of harmful substances that these bacteria produce.
In other cases, overgrowth of certain bad bacteria in the gut can cause the wall of the intestine to become overly permeable, allowing large molecules from food to pass through the intestinal wall into the bloodstream, where the immune system identifies them as foreign and mounts an inflammatory immune response against them.
Overuse of antibiotics is likely a large contributor to the Food Intolerance phenomenon, causing a reduction of bacterial diversity which often leads to a overgrowth of bad bacteria to occur. A good probiotic product may assist with the treatment of this condition, as it introduces good bacteria into the gut to work against any bad bacteria that may be resident.