Why does melting ice remain at 0 °C while it absorbs heat?

Melting ice remains at 0 °C while absorbing heat because the energy being added is consumed as latent heat of fusion rather than increasing the temperature of the substance.1

In a crystalline solid like ice, molecules are held in a stable, ordered lattice by attractive forces. As heat is applied, the temperature rises until it reaches the melting point (0 °C). At this stage, the added thermal energy is not used to increase the kinetic energy of the molecules—which would raise the temperature—but is instead used to perform the work required to overcome the attractive forces holding the crystal lattice together.1

This energy allows the molecules to transition from a fixed, ordered solid state to a more disordered liquid state. Because all incoming heat is dedicated to this phase change, the temperature of the ice and the resulting liquid water remains constant at 0 °C until the entire mass has melted.1