Dr. Nedumthottathil makes excellent points.
I would only add that cholesterol is an area where we desperately need more cross-disciplinary study. I've heard some cardiologists regard cholesterol as if it were the enemy and it must be obliterated. This drives the neuroscientists, who understand the importance of cholesterol to the brain, around the bend.
For example, serotonin is one neurotransmitter (neurotransmitters are the chemicals that carry messages from brain cell to brain cell) that depends on sufficient cholesterol. Without sufficient cholesterol (and serotonin), there is increased vulnerability to depression and anxiety.
Low cholesterol levels, far from always being something to celebrate, can also be symptoms of conditions such as hyperthyroidism, liver disease, manganese deficiency, malabsorption of nutrients from the intestines, and so forth.
We also need cholesterol to build and maintain cells, to produce sex hormones, to produce bile, and to convert sunshine to Vitamin D.
I find that this page from the Harvard School of Public Health provides a good education on good fats and bad fats.
http://www.hsph.harvard.edu/nutritionsource/what-should-you-eat/fats-full-story/index.html