A protein found in wheat and other foods, such as barley, some meat substitutes, rye, beer, pastas, and more. Gluten is naturally occurring and can be extracted and/or added to different food products. Reasons for doing so include altering texture, flavor, and modulating the amount of protein in a given food product. This can especially be important for processed foods, which have usually lost a lot of nutrients.
Now for the more scientific portion of the explanation. The human body contains different enzymes to digest different foods. One of these enzymes is protease, which is the protein that is meant to break down proteins. This enzyme does a pretty good job, but it does not completely break down gluten. The end result is that undigested gluten moves to the small intestine. Most people can handle the undigested gluten just fine.
Then there are people that have Celiac disease. Celiac disease is an autoimmune disorder where the presence of gluten in the small intestine triggers an immune response, thus damaging the small intestine. Damage to the small intestine is not necessarily permanent, but it usually means that people with celiac disease should eat strict gluten free diets. There are other autoimmune diseases that flare up in response to the presence of gluten, such as gluten ataxia (a neurological autoimmune disorder where consumption of gluten causes an immune response that attacks the brain). There are other items that could cause the bloating, diarrhea, headaches, and skin rashes that are sometimes associated with celiac disease, such as reactions to the fermentation of poorly digested carbohydrates.
Gluten is not an inherently bad item to have in your diet. If you are considering a gluten-free diet, do consider what items you are adding in for the items you are taking out of your diet. As indicated at the beginning of the page, a lot of processed foods can have next to no gluten. However, these foods can be far from healthy. For example, potato chips are gluten free.