Centering is an important concept in pilates. It comprises of finding your neutral spine and activating your deep tummy muscles to keep your spine in a safe stable position to allow you to move your arms and legs more efficiently. Neutral spine is different for everybody, as it depends on your individual spinal curves. Ideally you should have a small curve in the lower back. To find it you tilt your pelvis back and forth until you find the mid-point of the available range.
Your deep tummy muscles (transversus abdominis) are the only core muscles to attach directly to the spine via some fascia (tough connective tissue). It is thought that in people with back pain, the activation of this muscle is delayed. To activate this muscle imagine that you are drawing in your lower tummy, as if you are trying to squeeze into a tight pair of jeans.
By having a solid centre, you will be able to transmit force and movement through your limbs more effectively