Pilates engages and strengthens specifically the core muscles. Pilates is based on using your core effectively to achieve certain physical goals.
Adductors (inner thighs):
responsible for balance and explosive power
Glutes (buttocks):
stabilises and supports back
Abdominal Wall:
* Transversus Abdominus – lower abs
* Rectus Abdominus – middle abs which is your "8-pack"
* Obliques – side abs