Why are the ice cubes in your freezer foggy in the center, while other forms of ice, such as that made to make ice sculptures, are completely transparent?
The answer has to do with trapped air bubbles. Liquid H2O can hold a certain amount of air dissolved in it. Ice can also hold some dissolved air, but in much smaller amounts. Thus upon freezing, the water has more air than the ice can hold, and the excess air is ejected out of the freezing water. In the case of ice cubes in the freezer, the freezing process starts from the OUTSIDE and works its way into the center of the ice cube. The air that is ejected from the freezing surface is then ejected into the center of the ice cube. Since it can't escape, this air eventually forms trapped air bubbles inside the ice, causing it to look cloudy. Clear ice, on the other hand, is formed by directionally solidifying the ice, that is, freezing the water from one end to the other. This allows the excess air to be pushed from one end of the ice slab to another, eventually getting released into the air as the last of the water solidifies. Since the air was not trapped in the ice, its appearance is transparent. Variations of this technique are used to produce ice sculptures, ice cubes for restaurants, and many other applications in which clear ice is needed.
More information can also be found at How do you make clear ice cubes?