The picture is illustrating the idea we explored walking through the halls and going up and down the staircase. To improve on the model that I gave in class I have provided a slight slope to the hallways. This very minimal slope will carry or push the ball from one staircase to the next. This section of the trip is very similar to a piece of wire. A wire has a very small resistance and requires only the slightest voltage difference to push the current along.
We will usually neglect this and treat a wire as if it has zero resistance and therefore zero voltage drop. When the ball or person or electric charge reaches the staircase or battery there must be something to lift them up. Once on the top they roll to the other staircase or resistor and then give up their energy as the drop from a high height or voltage to a low height or voltage.