Tai Chi Chuan Yang Style
Tai Chi Chuan is the style that is practiced by more people than any other.  Tai Chi started out with twelve basic movements and kept expanding until it reached 108 movements.  All these movements are variations on the basic twelve.  The variations of movements allows you to exercise more muscles and joints and are called on to make more connections between various parts of the body.  This allows more practice of mind/body coordination, which helps in all aspects of daily life.  Tai Chi was and is, a martial art first and foremost. The name Tai Chi Chuan translates as Supreme Ultimate Fist.  Tai can mean Ultimate or Spirit, Chi mind or energy, Chuan body or form.  I have heard this translation to mean the form (Chuan) that allows the Universal Energy (Tai) to express itself (Chi). We practice Tai Chi Chuan in order to become more integrated with the energy of the Universe, to open and strenghten the body so that this energy can be channeled in an appropriate fashion.

Chen Style Taijiquan
Chen Style Taijiquan is the oldest system of taijiquan in existence andis the style from which all other styles of taijiquan are derived. It ischaracterized by its more explicit expression of spiraling energy in the body (often referred to as silk reeling energy) and transitions between slower smooth movements and sudden bursts of power. While the basic movements and exercises are simple and provide benefits to people of any age and physical condition, deeper study can also challenge a practitioner both mentally and physically, including both the martial and non-martial aspects implicit these in same movements.