Any object will be stable in its position if the line drawn perpendicular to the ground from the object’s centre of gravity falls within its base.
While walking on a rope, as the base is very thin (as thin as the rope), to be stable the artist has to move his centre of gravity appropriately. This he does by holding a bamboo pole horizontally or using an umbrella or just by spreading his hands.
When the artist feels that he is falling to his left, he moves the pole to his right (and the vice versa) and counters the forces disturbing his balance and makes the centre of gravity fall within his base.
Now one may ask, how does one sense these forces and maintain balance? This is achieved only by practice.