Conjoined twins are a result of a fertilized egg (zygote) either not fully separating in two or fusing back after separation.
Carolyn and Catherine Mouton were born as conjoined twins on July 22, 1953 in Lafayette, Louisiana. They were joined at the base of their spine and shared a common lower intestinal tract. Their lower vertebrae and sacrum were fused.
On September 17th, 1953 a team of eight surgeons performed the operation to separate the girls. Both girls went on to have healthy full lives. They were the first pair of modern day conjoined twins separated successfully.
Here is a video on Siamese twins.