Supplying thermal energy to a substance can do one of two things. It can raise the temperature, or it can change the state at constant temperature.
Specific heat capacity c is the energy needed per unit mass to raise the temperature by one degree. Specific latent heat L is the energy needed per unit mass to change the state with no change of temperature: fusion for solid to liquid, vaporisation for liquid to gas.
During a change of state the energy increases the potential energy of the molecules, not their kinetic energy, so the temperature stays constant. Vaporisation needs much more energy than fusion, because the molecules are separated completely and the vapour must push back the atmosphere.