Joseph Pilates "invented" his method of body conditioning during the First World War and then took it to America where he worked with dancers. It is a method of body conditioning which strengthens and tones muscles, and improves posture, flexibility and balance. The exercises strengthen your "core" muscles - those around your mid-section - predominantly your Transversus Abdominus, deep muscles which form a girdle around your body - hence Pilates being good for some back problems.
A class usually follows a pattern - finding correct posture, a few mobilising moves, a whole host of Pilates exercises, followed by a general stretch and a few minutes' relaxation. Sometimes people ache, sometimes they don't - and just because you don't, doesn't mean you're not doing the exercises properly or are not working hard. You will work on the deep muscles, possibly ones you didn't even realise you had! You will work with your breathing whereby slow, controlled, flowing movements are stressed.