What is "core muscle"?
Pilates exercises are designed to strengthen the "core" muscle of your body. Your body's "core" muscles are made up of the deep abdominal wall and the intrinsic spinal muscles, all of which are your foundation for movement. They include the muscles in your abdominals and back, the muscles in your pelvic floor and the diaphragm. Many of which can't be seen because they're buried underneath other muscles. All these muscles work together to keep your trunk stable.
Strong core muscles keep your back healthy. They hold your body upright, improve your balance allowing you to move your arms and legs freely. If the core muscles are weak, your body won't work effectively, and other muscles have to pick up the slack. Weak core is why we 'hunch' our shoulders or get an aching back.