We often think of our core as one spot hidden behind the naval. The true core, however, is multi-layered and spans the distance from the pubic bone to the solar plexus in front and in back on the body as well as side to side. The "core" is the deepest layer of abdominals, the Transverse Abdominus (TA for short), which lies beneath the External Obliques, Internal Obliques and the Rectus Abdominus.
In Pilates we often refer to the "Power House", which also includes the muscles of the back, the rib cage, the pelvic floor, the inner thighs, back of the hips and the glutes.