Because the heat absorbed by the Ice during melting at the melting point is used for phase transformation.
Melting is a phase transformation when a solid changes to liquid. When a solid is heated, it's temperature increases gradually till the melting point is reached. At melting point, the heat supplied is used by atoms and molecules to break away from the crystal lattice. In solids, the atoms and molecules are held in place due to strong attractive forces. Energy is required to break this force of attraction and leave the lattice. This energy is obtained by the molecules and atoms at melting point.
That's why temperature remains constant at melting point. The energy is used for breaking the lattice, instead of increasing the temperature.