The appendix (or vermiform appendix) is a blind-ended, worm-like pouch connected to the cecum and attached to the large intestine, near the junction of the small intestine and the large intestine. The appendix varies in length, but usually measures about 4 inches long in most humans.
The role of the human appendix has changed over the millennia, probably in response to changes in the human diet, as most humans have exchanged a diet rich in cellulose-dense plants (e.g., tree bark) for one that favors more easily digestible foods (e.g., a Big Mac and fries).
Although the appendix houses friendly bacteria and may still play a role in the immune system in modern humans, it is generally described as a vestigial structure (meaning that it has lost all or most of its original function through the process of evolution), and can be removed (by a procedure called an appendectomy) without any ill effects. As a result, some scientists believe that one day it will just disappear.1
1 This introduction to the appendix was compiled with a little help from Wikipedia.