1) The temperature of a substance remains constant during its melting point because this heat is used in changing the state of the substance by overcoming the forces of attraction between the particles in the existing state.
2) Example, when we heat ice, then the heat energy we supply is absorbed by ice without any rise in temperature. This is because, the heat absorbed in the contents of the beaker.
3) Similarly, the temperature of a substance also remains constant at its boiling point until the complete substance boils. When we supply heat energy to water, particles gain more kinetic energy and then they move faster. And, slowly, the particles overcome the forces of attraction and at this point, the liquid starts changing into gas at this point. This is called the boiling point