Push hands is the Tai Chi version of sparring. Most often it is used as a bridge between the forms of Tai Chi, (the slow dancelike movements that you see people doing when they practice Tai Chi) and the martial arts aspects of Tai Chi. (Don't be fooled, as is mentioned here, speeded up Tai Chi is a deadly martial art, Advanced students often win full contact Kung Fu competitions). Push hands is sort of a balance game, one person tries to cause their partner to lose their footing or balance. There is a constant soft flow of pressure and give from one person to the other, striking is not allowed. It teaches excellent balance and hand speed and is great preparation for a "real fight" which is often conducted very quickly and at close quarters. Push hands is very relaxing and intimate, it creates a very calm instinctive state that allows you to react correctly without conscious effort.