Here's a nice little article on what push hands is all about, for those who might not think tai chi is any sort of martial art:
In general, players stand facing each other with their hands in light contact with each other’s arms. As one person’s arms move, the other person follows the movements, keeping both hands in contact at all times. A player may push against the other person’s arms, chest, shoulders, or waist; the person receiving the push yields by turning the waist and redirecting the pusher’s arms in a variety of ways. Pushing and yielding continues in a circular fashion until one person is “uprooted,” with one or both feet losing contact with the floor; then the cycle continues. If you were to watch two skilled push-hands players in action, you may see virtually no movement, as each person gently feels for a point of tension in the other person’s body to push against. All at once, someone’s hand will move, the other person will stumble, and the two partners will smile and begin again.full article here