There are many reasons people choose a gluten free diet, but today I'm just going to talk about what gluten is, and why it can be an issue for some people.
So what is Gluten? According to Wise Geek, gluten is a protein found in rye, wheat and barely. In bread making, gluten provides many qualities. Gluten helps make bread elastic, or flexible, providing that chewy texture when eaten. Gluten also keeps the gases that are released during fermentation in the dough, so the bread is able to rise before it is baked. Gluten also firms up when it is cooked, and helps ensure the bread maintains it's proper shape.
The cross breeding of wheat has occurred for many reasons. These reasons include high grain yield, good quality, disease and insect resistance and tolerance to stresses. It is thought that this cross breeding is resulting in more gluten in the wheat itself, and creating more health issues like celiac disease and wheat allergies. This hybridization is a completely unnatural process in wheat, as wheat itself has a complete flower, and can pollinate itself. According to Wikipedia, chemical hybridizing agents are used to selectively interfere with pollen development to allow cross pollination to occur.
There is also another train of thought that it is not the Gluten that is causing the allergies and disease, but wheat lectin instead. I will do more research on that later.