Let us first review some fundamental digestive anatomy associated with this question. Please refer to the provided link. The gastrointestinal anatomy can be thought of as a tube within a tube within a tube... etc. As soon as food or drink enters this tubular system via the mouth, a complex series of physical and chemical processes are set in motion to extract nutrients from this food as well as facilitate the downstream elimination of wastes. Food moves via the mouth, esophagus, stomach, small intestine, large intestine, and rectum, where solid wastes are eliminated. It happens in that order. For this question, one should focus on the tail end of this solid waste elimination process which includes the small and large intestine.
A stomach rumble is what clinicians refer to as a bowel or peristaltic sound. The rumble sound that one hears is actually the noise that is generated when the contents of the gastrointestinal system are propelled from the small intestine to the large intestine. This movement is facilitated by a series of muscle contractions. The smooth muscle lining these areas propels the solid wastes downstream through this tubular system. The scientific term which is used to describe this process is peristalsis.