See explanation below.
At a change of state, all the energy supplied is used to break the bonds between the particles. The energy supplied does not increase the kinetic energy of the particles.
Since temperature of a substance is dependent on the kinetic energy of the particles, at a change of state, there is no change in temperature.
Water at 100C will have less energy than steam at 100C because in order for water at 100C to change to steam at 100C, more energy, called the latent heat, is required.
Technically water at 100C and steam at 100C have the same amount of kinetic energy. It is the potential energy that is being increased (gases have more potential energy because their particles are further apart than liquids).
I hope I'm not oversimplifying it, but average kinetic energy is directly proportional to temperature:
Basically, an increase in