Think of ice melting like a crowded dance floor where the music (heat energy) starts playing; the molecules finally get enough energy to break their rigid formation and start flowing around each other.

Phase transition occurs when the kinetic energy of the molecules is sufficient to overcome the intermolecular hydrogen bonds holding the crystalline lattice of ice together. At $273.15 \text{ K}$, the rate of melting and freezing reaches a dynamic equilibrium. Adding heat provides the necessary latent heat of fusion to complete the state change without increasing the system's temperature.

Always remember that for most substances, $0°\text{C}$ is not absolute zero; standard exam questions often test the conversion between Celsius and Kelvin by adding or subtracting $273.15$.