Question

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

Answer 1

The temperature of a substance remains constant while melting, or boiling, as the heat provided by the flame is converted into energy to alter the bonds between the molecules of the substance.Altering the bonds, in the sense, breaking the bonds between the molecules, so that the substance may flow freely, or strengthening the bond, to make the substance less flowing, during it's conversions from solid, liquid, and gaseous phases.It is also called latent heat, or hidden heat.

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Answer 2

States or phses change during melting and boiling of a substances , Temperarure remain constant here...

The heat given to the substance to overcome the intermolecular interaction between the Particles of the substances...
This heat doesnt increases the temperature, it actually increases the distances between the particles of a substances which result the change in state of a substances...

As this heat is not captured by thermometer , and so is hidden..and so called Latent Heat...