The structure you are referring to is the appendix. It is a small, tube-like structure that is attached to the cecum, which is the beginning of the large intestine.
The appendix is primarily composed of lymphatic tissue and plays a role in the immune system, especially in the development of gut-associated lymphoid tissue (GALT). While its exact function in humans is not entirely understood, it is thought to contribute to the maintenance of gut flora and the immune response.
In some cases, the appendix can become inflamed, a condition known as appendicitis, which may require surgical removal. Despite being deemed as a vestigial organ by some, recent studies suggest it may have a role in supporting good bacteria in the digestive system.