Which organ stores and compacts waste before it is eliminated?

That organ is called the rectum, or more coomonly, the anus. The rectum is the final part of the large intestine and the digestive system, where food that has had all its nutrients extracted (as much as possible, anyway) is sent to be compacted and sent out through the anus in the form of excreta. The contents in the rectum is mostly indigestible fiber and other materials. The rectum at its end connects to the bodily orifice known as the anus.