Pilates can be done with or without the Reformer, but the design of the Reformer is incredible, since some heavy models sit in large gyms (above), while others can easily be slid under a bed or folded and rolled into a closet (below). The main premise is lying on a bench and using bands and pulleys to strengthen the core, while stretching and strengthening other muscles. It allows an individual to do several exercises while laying down, sitting, or kneeling which makes it perfect for those that have an injury or too much pain to stand up and exercise.
The beauty is that this machine can work every muscle while still, in the case with many of the designs, be put away when guests come by. It can be ideal for someone living in a small apartment or someone without an extra exercise room, but still wants a full body workout.
My personal experience is with a foldable Aero Pilates 5 cord machine from HSN (similar 4 cord model here). I have back problems and very tight hamstrings and calves from doing a desk job everyday and this was the best way to stretch them, while still doing resistance training. This can provide a full body workout low impact workout. The version I have is foldable, so it can be folded and rolled into a closet. If you remove three pieces, it can fit under a bed, as well.