The elimination of cholesterol from your body is done through the bile.Where does bile come from and how is it produced?  What is its biological importance?
The bile is produced from your liver, and its biological importance is to emulsify fats from the other contents of your small intestine. Through this, much of the fats in your diet are separated, and they are acted upon by the enzymes, lipases, for proper digestion. Without the bile, it will be very hard to digest the fats that you take in from your diet.
Once formed in the liver, your bile goes to the gallbladder, and it is stored and concentrated there. When you eat, bile is released from your gallbladder and goes to your small intestine, where it will emulsify the dietary fats for proper and efficient digestion.

Your bile has four organic components:

Bile acids
One of the components of your bile are the bile acids, which are formed and synthesized from cholesterol. Thus, without cholesterol, you cannot form bile. If you look at the chemical structures of bile acids and cholesterol, you could easily and immediately say that they are related structurally. To a large extent, cholesterol is eliminated from your body, as bile is poured into your small intestine and eliminated through your fecal matter.

Phospholipids
The second most abundant component of your bile are the phospholipids, with lecithins being the most prevalent ones. In combination with the other components of bile, phospholipids help to solubilize other fats that are present in your diet, resulting in improved digestion.

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Cholesterol
Cholesterol is the third component of your bile and makes up around 4% of the total solids in bile.  The presence of cholesterol in bile is a biological means of eliminating it from your body.

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Bile pigments
Bile pigments contribute to around 2% of the solids of your bile. It has no specific function, with the exception of providing a color which is yellow to orange and turns green when oxidized. Cholesterol is eliminated from your body through two ways: when it is used for the synthesis of bile acids which are subsequently lost in the gastrointestinal tract or when cholesterol is used as a component of your bile, which is subsequently lost in the gastrointestinal tract.