The digestion of fats primarily occurs in the small intestine. Bile produced by the liver and stored in the gallbladder is released into the small intestine, where it emulsifies fats, breaking them down into smaller droplets. This process increases the surface area for pancreatic lipase to act on, further breaking down the fats into fatty acids and glycerol which can then be absorbed by the intestinal lining. The small intestine is thus the major site for the digestion and absorption of dietary fats.
Reference:
Gastrointestinal Physiology by Leonard R. Johnson
Human Physiology: From Cells to Systems by Lauralee Sherwood