How is latent heat of vapourisation utilized in changing state?
It is raising the energy level of the system by breaking the bonds that hold it together as a liquid. Once the bonds are all broken within a certain volume, the liquid will vaporize. 

The energy seems to 'disappear' or 'hide' because we expect to see a change in the properties of the chemical as energy is added, but the breaking and reforming of intermolecular bonds is happening constantly within a liquid. 

When the liquid has enough energy, random bond-less distributions will occur within the liquid that are large enough to overcome the pressure of the liquid and its container. This is how water boils. If enough of the water molecules become unbound, they will form a bubble. Inside the bubble, the water vapor will be exactly equal to the pressure of it's environment.

This gives us our definition of boiling point: vapor pressure equals atmospheric pressure. The water or other liquid can't stay in the liquid state because there's not enough surrounding pressure to hold it together.