Mammals move by using contractile muscles that pull against attachment points in their rigid internal skeletons, causing the bones to change orientation relative to each other around specific joints. This muscle contraction directly affects the movement, as the muscle pulls in a linear fashion in the direction the mammal wants the bones to move. This method of motion is shared by all vertebrates with internal skeletons.
Mammals use this method of motion is a variety of ways, enabling them to crawl, climb, run, jump, fly and swim. Each of these movements has several variations as well, except for flight which, among mammals, is done only by bats. Mammals are found nearly everywhere on Earth where air is accessible. Their musculoskeletal design works so well that the largest animals on land and in the water are mammals.
This is not the only type of movement in the animal kingdom, however. Arthropods, such as crabs and insects, have an exoskeleton, and they use attachment points on these shells, rather than on internal bones, as the basis for movement. Because of this orientation, arthropod muscles actually pull the opposite way they need the joint to move, rather than in the same direction as with an internal skeleton.