Cats are very flexible agile creatures and have a certain elegancy about them...most of the time.
Cats are capable of walking very precisely because like all felines, they directly register; that is, they place each hind paw (almost) directly in the print of the corresponding forepaw, minimizing noise and visible tracks. This also provides sure footing for their hind paws when they navigate rough terrain. The two back legs make the cat able to leap far distances and fall from high places without getting hurt.
Cats possess rather loose skin; this allows them to turn and confront a predator or another cat in a fight, even when it has a grip on them
The tail is used as a counterbalance to the body during quick movements. And to keep balance for the animal.
Cats also have free-floating clavicle bones, which allows them to pass their body through any space into which they can fit their heads.