Many of the movements you see in the Cirque du Soleil performers are just the result of natural flexibility and dedicated training. Some have natural flexibility we refer to as joint laxity. Most have been involved in gymnastics and/or dance from a very young age, which has helped mold and shape the joints to accommodate extreme movements.
You may also notice that many of the performers are Asian women. Young, females of black and Asian origin appear to have natural hypermobility (loose ligaments in the joints). This also contributes to their ability to look like body contortionists.
People with generalized joint laxity may be born with some differences in the connective tissue that account for this degree of looseness. There are at least 18 different types of collagen fibers making up the various soft tissue structures in the body. It may be that joint laxity is the result of changes within the collagen structure, a different type of collagen fiber in the joints, or a combination of both.
Scientists are studying these differences in hopes of helping to prevent joint injuries in young athletes as well as prevent joint stiffness as we age.