What is "hard water", and why does "hard water" leave more deposits in hot water pipes than in cold water pipes?
"Hard" water is water with lots of dissolved minerals, specifically calcium and magnesium. Hard water is not a health risk, but a nuisance because these minerals build up and are left behind.
This is because it is easy to dissolve things in water: water, in other words, is a good solvent, and therefore picks up impurities easily. Pure water -- tasteless, colorless, and odorless -- is often called the universal solvent.
As water moves through soil and rock, it dissolves very small amounts of minerals and holds them in solution. Calcium and magnesium dissolved in water are the two most common minerals that make water "hard." The degree of hardness becomes greater as the calcium and magnesium content increases: and that depends on what area you live in.
The answer to your question is that heating water separates the water molecules from their dissolved minerals: if you imagine, for example, boiling a salt solution in a pan, the water would turn into steam and boil off, leaving only the salt. In the same way, heated hard water forms much more scale of calcium and magnesium minerals (limescale deposits) than cold water does: simply because the heat encourages the minerals to separate from the water.
It is water which has a high mineral content, consisting of dissolved minerals, ranging from calcium and magnesium ions present in it, but it proves to become a nuisance as it damages the water pipes by scaling and corroding the pipes it come into contact with. Water that contains a pH value of above 7 is known as hard. Heating water seperates the water from the dissolved minerals are left behind as sediments or deposits, so hard water that was being heated contributes to the deposition of more minerals in hot water pipes than cold water pipes, given the above point.