When ice melts, its crystalline structure dissolves. The water molecules, formerly locked in a hexagonal lattice, gain enough thermal energy to break free. They slide past each other. The solid becomes a liquid. The structure is gone, but the molecules remain.
This is a phase transition, and it is among the most fundamental forms of dissolution in the physical world. Boiling is another: the liquid dissolves into vapour, the molecules escaping the surface entirely. Sublimation — the direct transition from solid to gas — bypasses the liquid phase altogether. Dry ice does not melt; it dissolves directly into the air.
Phase transitions are reversible. Freeze the water and the lattice reforms. Condense the vapour and the liquid returns. The dissolution is a change of state, not of substance. But the reverse transition does not produce the same ice — the crystal will have different defects, different grain boundaries. The dissolution, though reversible, is not perfectly so. Something is always lost in the transition: the particular arrangement, the specific history. The substance returns; the structure does not.