When heat is supplied to a solid, say ice, it starts melting. But temperature does not rise even after continuous supply of heat until all ice melts. The extra heat supplied, is used in melting of ice, which is called latent heat of fusion.
Similarly, when a liquid, say water, starts boiling the temperature of water does not rise instead of continuous supply of heat. The extra heat supplied to the boiling water is used in the vaporisation of water, which is known as latent heat of vaporisation.
That’s why, the temperature of a substance remains constant during its melting or boiling point.