Your first statement is very ambiguous so I will give it the best shot as to what you are saying.
The temperature, between the point of ice melting and water boiling, is increasing as water is in its liquid state.
Now during a phase change, or while the water is boiling, the temperature remains constant because the energy being added is being consumed to complete the phase change.
But if you're looking at the phase change graph, the points of positive slopes, are moments when energy is increasing as the water, in whatever state, is increasing. But when the slope of the graph is 0, the water is changing phases and the temperature remains constant! I hope I explained that so you could understand it, and I hope this helps you!