Final answer:
The ileocecal valve is the sphincter that opens to allow undigested materials to pass from the small intestine into the large intestine, responding to increased ileum motility and regulated by nerves and gastrin.
Step-by-step explanation:
The valve that controls the movement of undigested material from the small intestine into the large intestine is called the ileocecal valve. This particular sphincter is generally constricted and it opens in response to increased motility in the ileum, allowing the chyme to pass from the ileum into the cecum, the first part of the large intestine. The relaxation of the ileocecal sphincter is regulated by both nerve signals and the release of the hormone gastrin, which occurs when there's digestive activity in the stomach. In addition to preventing backflow into the small intestine, the sphincter ensures that by the time your next meal is ready to be digested, the previous meal has been moved through the stomach and small intestine completely.