The skeletal system is the system of bones in an organism's body that gives it structural rigidity. Also often included in the skeletal system are the cartilage, ligaments, and tendons that connect all of the bones together as well. The human skeletal system is composed of 206 bones. Human babies are actually born with many more bones (closer to 300) but over time some of them fuse together to make a total of 206. It is divided into two major parts. The axial skeleton is composed of 80 bones and comprises the backbone, rib cage, and skull. The appendicular skeleton is composed of 126 bones and is comprised of everything else (pelvis, pectorals, and extremities).
As a side note, most animals do not have internal skeletal systems (in other words are invertebrates instead of vertebrates). Only about 2% of animals are classified as vertebrates.