When you buy eggs from a supermarket there is a pretty good chance your eggs have been in that carton for almost a month. Commercial egg farmers have 30 days once their eggs are packed in a carton to sell them. If the carton is labeled with a "use by" date that date is 45 days from the when the eggs were packaged. Assuming the eggs were packaged the day they were laid, that is still an egg that has been sitting for a while. The longer the eggs sit the more the membrane beneath the shell separates from the shell, making peeling easier. The trade off is the longer the eggs sit the less centered the yolk will be because the whites become less dense (also the longer eggs sit the less nutrition they provide).
Now you want to make a beautiful platter of deviled eggs with nice neat whites and centered yolks... what to do?
It's as easy as stopping by the local farm market and buying some fresh free range eggs from a local farmer and following these steps to perfectly boiling your fresh eggs. (or go one step further and put some happy hens in your backyard, but that is an instructable for another day)