Without bile, you'd have a heck of a time digesting fats. Fats need special assistance in being digested because they don't dissolve in water. They're inclined to stick together, forming large clumps. Have you ever mixed oil and vinegar to make salad dressing?
You will likely end up with separate pools of vinegar and oil on your lettuce. That's how the fats in your digestive tract are with water. The two won't mix. Lipase, the enzyme that digests fat, doesn't stand much of a chance against large masses of fat. Unless broken down first, a lot of the fat we consume would pass through our digestive system without being absorbed.
If fat isn't absorbed, then the fat-soluble Vitamins A, D, E, and K aren't absorbed either. Fat also fuels many of our body's cells, not to mention that if it's not absorbed, it will cause bloating, gas, and diarrhea. One of bile's jobs is to emulsify fats, meaning it enables fat and water to mix. Bile contains molecules that are partly attracted to fat and partly attracted to water. These molecules draw fat and water together by sandwiching themselves in between the two. Thus, fat molecules are kept separated, and lipase is able to digest them.