Gluten is a composite of the proteins gliadin and glutenin. These exist, conjoined with starch, in the endosperms of some grass-related grains, notably wheat, rye, and barley. Gliadin and glutenin comprise about 80% of the protein contained in wheat seed. Being insoluble in water, they can be purified by washing away the associated starch. Worldwide, gluten is an important source of nutritional protein, both in foods prepared directly from sources containing it, and as an additive to foods otherwise low in protein.
The seeds of most flowering plants have endosperms with stored protein to nourish embryonic plants during germination, but true gluten, with gliadin and glutenin, is limited to certain members of the grass family. The stored proteins of maize and rice are sometimes called glutens, but their proteins differ from wheat gluten by lacking gliadin. The glutenin in wheat flour gives kneaded dough its elasticity, allows leavening and contributes chewiness to baked products like bagels.
Although wheat supplies much of the world's dietary protein and food supply, as many as 0.5% to 1% of the population of the United States has celiac disease, a condition which results from an inappropriate immune system response to gluten. The manifestations of celiac disease range from no symptoms to malabsorption of nutrients with involvement of multiple organ systems. The only effective treatment is a lifelong gluten-free diet.
Note that wheat allergy and gluten intolerance are not the same thing.