What is gluten, and why would gluten be bad for you?

As far as I know, gluten is simply a structural protein found in wheat, which is useful in making bread rise.

Several food companies seem to be promoting gluten-free foods and gluten-free diets. What does gluten do that people are concerned about?

Is gluten actually a structural protein, or does it have other biological functions?

Are there any legitimate reasons to go on a gluten-free diet, such as medical conditions? Or is most of the gluten-free craze a result of marketing?

I’m asking this question because I’ve seen a lot of gluten-free products on supermarket shelves lately. The advertisements heavily imply that gluten is harmful, although I am not aware of any reason that this would be a case.