Which organ in the body responsible for the storage of bile?

The gallbladder is the sac-like structure under the liver that stores about 30-50 ml of bile. The liver produces bile, and the gallbladder stores it. From there it is excreted, travels down the bile duct, where it passes through the pancreas, which produces lipase (which does break down fat), before it goes into your small intestine. The gallbladder releases bile into the duodenum, part of the small intestine, to aid in the digestion of fats. Bile emulsifies the fats, or breaks them into smaller particles, to assist in their digestion. If the bile salts crystallize, you get gallstones.

The gallbladder will release bile only under the influence of cholecystokinin. When the chyme (food leaving the stomach after processing) passes through the plyoric sphincter (valve muscle connecting the doudenum to the pylorus (bottom part of stomach), this hormone is released, and the bile is released into the doudenum through a series of ducts that also lead from the pancreas, so the enzymes for further digestion can enter as well.
Common Bile Duct
small intestine
Although the gallbladder does not make the bile, it is where the bile is stored.
The gallbladder stores bile in the body until it is needed in the digestive process. When spicy or fatty foods are eaten, the gallbladder will release the bile into the stomach to help with the digestion.