This response is from AP Chem class experience.

Phase change is due to differences in pressure and temperature. When a state changes due to pressure and temperature an odd phenomena happens. Let's suggest water for an example. When water is subjugated to heat or decreased pressure it often evaporates. But in addition, when water evaporates it also absorbs heat and increases pressure by taking up more volume. That means when their is excess heat or space to fill, water will evaporate removing the excess heat and space from the system until all the water has been evaporated or that their is no more excess heat or space. If you run out of excess heat or space first then you have a system that both includes water and water vapor. You would call this point of temperature and pressure the "vaporization point." If more heat is added, raising the temperature, more water would evaporate lowering the temperature to the point it was at before. The two different systems would exist at the same temperatures and pressures, but the second system would have more heat. The two systems are able to remain at the same temperature and pressure, because the excess heat created more vapor in the second system than the first.

Your question is "Why don't the properties gradually shift from one to the other in a relationship with the temperature?" The truth is that the properties do not gradually shift from one to the other in a relationship with temperature, but they do with heat. At first, in water, heat is added to water increasing its temperature. This continues to a point where the temperature becomes to great for the individual water atoms to hold so they each separately absorb enough heat to convert to gas, lowering their individual temperature to the temperature of the system. This continues till all the water atoms have been vaporized, and then the increase in heat continues to increase temperature again. Temperature is not what controls phase change; heat is. Think of the vaporization point merely as a scheduled stop on the path of increasing temperature to slowly cross a bridge between liquid and gas. On this hike to increase temperature, energy is still required to cross the bridge, however, no distance towards higher temperature is being traveled at this point because the bridge needs to be crossed to pass this point.

An interesting example of this in nature is the increased severity of vapor burns. Water and water vapor can be at the same temperature, yet burns from water vapor are always more severe. Why is this? Because even at even temperatures, the water vapor contains more heat. When someone is burned by water, the water is quickly evaporating reducing the heat transferred to the unfortunate victim and instead having it be used for a phase change. However, when steam burns someone, all of the heat is transferred to the victim creating more danger.