Boiling is appropriate for some applications, simmering for others. Below are some quick guidelines:
Boiling is good for:
1. Pasta – to keep the pasta constantly moving (so it doesn’t stick) and to speed up cooking time
2. Non-starchy, non-delicate vegetables – to speed up cooking time. Vegetables need to be cooked quickly to preserve their color and texture.
Simmering is good for:
1. Animal proteins like meats and eggs – this is due to the nature of their proteins – at higher cooking temperatures, more moisture is squeezed out as the proteins contract causing the eggs/meat to be tough. Remember this when making hard boiled eggs or when poaching chicken for chicken salad.
2. Starchy vegetables like potatoes as well as delicate vegetables like brussels sprouts – boiling water is too rough and causes the vegetable to break apart.
3. Long cooking vegetables like beets are also better at a simmer – since it takes a long time for the center of the vegetable to come up to the same temperature as the exterior.
A few other tips:
What is the difference between boiling, rolling boil and a full boil? For cooking purposes, these all generally means the same thing.
What is poaching? Cooking -usually animal protein – in barely simmering water. Remember that proteins don’t react well to boiling so keep it at a very low simmer – like…barely bubbling at all.
Always start with cold water – It is often recommended to bring a pot of cold water to a boil or simmer, not warm/hot water. The reason for this is that the warm/hot water can pick up off flavors from your pipes and your hot water heater. So…it is best to start with cold water.
Hope this helps improve your cooking! 
Santogold (Santigold)
Catching Fire (The Second Book of the Hunger Games Trilogy)
