Why does the temperature of a substance remain constant during its melting point or boiling point?

The temperature of a substance remains constant at its melting and boiling points until all of the substance melts or boils because, the heat supplied is continuously used up in changing the state of the substance by overcoming the forces of attraction between the particles. This heat energy absorbed without showing any rise in temperature is given the name latent heat of fusion/latent heat of vaporisation.