Basically, while a substance remains in a specific state, the particles do not attempt to separate themselves from one another that much. The energy used from heating is channeled to the vibration of the particles in their positions.

This proceeds until such time when a substance attains its furthest limit - the melting or the boiling point. In this case, this is the time when the particles attempt to break apart from the inter particle forces connecting one another. This separation requires more energy than the vibration energy. Thus, all the heat channeled is used solely to separate the particles, without any energy channeled to the vibration of the particles. As such, there is no temperature change during such phases.

from time = 1min to time = 3min, the energy supplied to the solid molecules is used to break the intermolecular bond between the solid molecules to become liquid molecules, instead of increasing the temperature of the substance.

done