Which is the best interpretation of the two flat portions of the graph?

In those portions, the heat supplied to the substance by the heater does not lead to a temperature rise as intermolecular forces are broken.

When a substance is heated, we normally expect that its temperature will rise as a consequence.

However, heat may be supplied to a substance but its temperature does not rise owing to the fact that the heat energy supplied is used to break intermolecular bonds.

This occurs during fusion and boiling. The heat supplied at these point does not result in temperature rise since it is used to break intermolecular bonds. The temperature remains steady during these processes as shown by the two flat portions on the graph in the image attached to the question. This heat supplied is known as the latent heat.

For more about latent heat, see: