digestive system - By what mechanism does coeliac disease cause excess fat in the feces?

Alan has covered some of it, but to add an illustration of the malabsorption piece of it, below left you can see a "normal" slice of small intestine, where the villi (finger like projections) are covered in enterocytes (the purple "bricks" along the border of the finger), which are responsible for the uptake of lipids (and their eventual "packaging") after they have been emulsified with bile salts in the intestinal lumen.

The offending gluten causes an autoimmune reaction over time that damages these villi as well as the enterocytes (as seen on the right side of the diagram), leaving a flattened area (hence far less surface area for absorption), and disrupted lipid packaging, so the unabsorbed lipids continue through the intestine into the stool.

from Cell Biology at Yale