It is dissolved air. If you run the cloudy water into a glass you will see that it clears first at the bottom as the bubbles rise to the top.
The reason this happens is that unlike most soluble solids, gases become LESS soluble as the temperature rises. As the water is heated, the amount of air that can stay dissolved becomes less and the excess tries to come out. The water in the hot water pipe is under pressure so this excess is held in solution until you open the tap and it then instantly appears as minute gas bubbles. Much like opening a bottle of fizzy lemonade.
The same thing can happen to water in the cold pipe in summer when cold water from the mains moves into pipes above ground (in the home) where it warms up.