Boil water first when cooking what foods?
There is no single universal answer to this question, as it depends on the specific food and outcome desired, but there are a couple of common themes that influence whether starting from cold water or boiling water is the preferred method:


Larger foods that need to cook through may overcook on the outside before the inside is cooked, if started in boiling water.  For example, potatoes are usually started in cold water so that they cook through to the center.
Some foods contain enzymes that will be deactivated at boiling temperatures, but may act more quickly at lower temperatures.  Starting in boiling water would be for when it is desirable that the reactions be inhibited; starting in cold water facilitates the reactions continuing. 
Sometimes it is simply for precision to get a repeatable recipe.  Boiling water is always the same temperature (at least for a given altitude), so beginning cooking at the boil is reliable and repeatable compared to starting with cold water which may have an unknown temperature curve as it comes up to the boil.