If our livers didn't produce bile, humans would have a very difficult 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.
One way to think about this is to consider oil and vinegar in a salad dressing. They don't mix very well, and end up as separate pools on the lettuce. This is how the fats in our digestive tract are with water.
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 wil 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 sandwhiching themselves in between the two. Thus, fat molecules are kept separated, and lipase is able to digest them.