Lime water is the common name for saturated calcium hydroxide solution. It is sparsely soluble. Its chemical formula is Ca(OH)₂. Since calcium hydroxide is only sparsely soluble, i.e. ca. 1.5g per liter at 25°C^[1], there is no visible distinction to clear water. Attentive observers would notice a slightly earthy smell. It is clearly distinguishable by the alkaline taste of the calcium hydroxide. The term is based on the mineral sense of lime, rather than the fruit sense of lime. When exposed with carbon dioxide, lime water turns into a milky solution.

While lime water is a clear solution, milk of lime on the other hand is a suspension of calcium hydroxide particles in water. These particles give it the milky aspect. It is commonly produced by reacting quicklime (calcium oxide) with an excess of water - usually 4 to 8 times the amount of water to the amount of quicklime. Reacting water with quicklime is sometimes referred to as "slaking" the lime. The calcium oxide will convert to the hydroxide according to the following reaction scheme:

CaO + H₂O → Ca(OH)₂

This reaction is strongly exothermic and will generate enough heat to bring the suspension to a scalding temperature. At a ratio of 2 parts water to 1 part lime (by weight), the generated heat is sufficient to bring the suspension, i.e. the water in it, to boil. Milk of lime is an alkaline with a pH of 12.3. It is commonly used in the chemical industry and as a neutralizing agent in municipal waste water treatment. While it has a multitude of other uses, it is best known in its (historical) use as a paint: lime wash or whitewash.

abstracted from: http://en.wikipedia.org/wiki/Lime_water