A natural childbirth is where no invasive techniques or medications are used during labour and delivery. Instead, techniques such as breathing exercises, self-hypnosis, and massage are all used for pain management instead of medications such as with an epidural. Some women feel very strongly about having a natural childbirth and in most circumstances this can be achieved; however, it is important to be aware of the scenarios where intervention is necessary to prevent harm to the mom or the baby. See this post for when this may be the case.
For more about having a natural childbirth, read this post.