Symmetrical balance is basically a mirror image. It is easy to achieve and contributes a sense of order, predictability to a room, and has a more formal/refined feel.
Symmetrical Balance. If you divided the room in half, it would mostly be a mirror image of itself. Also, note how the coffee table appears to be small in scale without much mass, despite its actual size. Photo from April 2007 "Architectural Digest".Asymmetrical balance is using objects of differing size to achieve a balanced scheme. This is a bit trickier to obtain, and takes a lot more practice to achieve. It involves arranging objects of different mass and scale to form a pleasing arrangement. Asymmetrical balance creates a more informal feeling in a room.
Asymmetrical balance. While the furniture is arranged symmetrically, notice the groupings on the mantle are not. They are arranged in a way that the heights and colors of object are balancing, as opposed to being identical sizes, etc. Photo from May 2007 "Architectural Digest".
Radial balance is balance found in objects radiating from a central point.