The origins of Pilates as we know it today has been well documented as the mind and body exercise methodology developed by Joseph Pilates over his lifetime.  Motivated by his own ill health in his younger years Joseph found methods of using exercise to improve his own health and well being.
Whilst in an English internment camp in World War 1 Joseph rigged springs above hospital beds that would allow patients to begin rehabilitation while still lying in bed. 
After moving to the US in 1923 Joseph opened a studio in New
York and developed a series of mat exercises design to build abdominal strength and body control. He then went on to design and build a number of apparatus, including the Universal Reformer.
Pilates builds the "Powerhouse" ( abdominals, butt, back, inner thigh muscles).  
Today we might call it "the Core".
Pilates is founded on Eight Great Principles:
  • Control
  • Breath
  • Flowing movement
  • Precision
  • Centering
  • Stability
  • Range of motion
  • Opposition
Pilates is:
  • Fitness
  • Mobility
  • Strength 
  • Physical
  • Rehabilitative
  • Restorative
 The Pilates Method teaches you to be in control of your body not at its mercy.     
  Joseph Pilates