Why does a phase change graph have horizontal lines?

Flexi Says:
A horizontal line on a phase diagram shows how as temperature increases at a constant pressure, the substance changes from solid to liquid to gas. As one moves left to right across the red line on the graph below, the temperature of the solid substance is being increased while the pressure remains constant. When point A is reached, the substance melts and the temperature B on the x-axis represents the melting point of the substance at that pressure. Moving further to the right, the substance boils at point Y and so point C on the x-axis represents the boiling point of the substance at that pressure. Different horizontal lines can be drawn to find the melting and boiling points at other constant pressure values.
General phase diagram, which shows the state (phase) of a substance as a function of its temperature and pressure.