Ice cubes melt as the molecules of air, water or other substances around the ice transfer heat into the molecules of the ice itself. As the temperature increases, the bonds change inside the ice, entering a liquid phase and turning into water, according to About.com.
Within ice cubes, not all of the solid crystals are aligned precisely with one another. At these junctures, the atoms start to move, a trend that then spreads throughout the crystal, turning the parts that had orderly alignment into chaos as well, according to Live Science. The implication is that there may be liquids inside crystals that have not yet reached the melting point, but Live Science explains that further study is necessary to verify that claim.
Ice cubes tend to melt more quickly in water than if they are left out on a surface at room temperature, even if the water is slightly colder than the room. The reason for this is that the bonds in water at a liquid phase interact with the crystal structures of the ice more effectively than air alone. While heat transfers into the ice from the air, it does so more quickly from liquid. Therefore, dropping ice cubes into a glass of water leads to faster melting than setting those cubes out on the kitchen counter and waiting for them to melt, according to About.com.