Gluten is a form of plant protein found in the grains wheat, barley and rye, and in foods containing ingredients derived from these grains.
While it's possible to have a true allergic reaction to the gluten protein in wheat, such an allergy is generally referred to as a wheat allergy, not a gluten allergy. Unofficially, though, many people use the term "gluten allergy" interchangeably with the terms celiac disease and non-celiac gluten sensitivity, two separate conditions that involve two different immune system reactions to gluten.
Neither celiac disease nor non-celiac gluten sensitivity is technically an "allergy" allergies generally involve near-immediate symptoms such as sneezing and itching, while reactions to celiac and gluten sensitivity are more often delayed and involve gastrointestinal and neurological symptoms.
But as awareness of the gluten-free diet has grown, some people with celiac or gluten sensitivity have found it simpler to tell people that they have a "gluten allergy" rather than take the time to explain their conditions. The treatment for celiac and gluten sensitivity total avoidance of the offending substance is the same as the treatment for an allergy, and people who aren't familiar with gluten-related conditions may have an easier time understanding the term "allergy."