If you wait until an egg is completely cool the skin sticks to the egg and makes it harder to peel . After the egg is cooked, run some cold water over it until it's cool enough to handle.As you peel the shell off, pull the skin of the egg up with it and the shell will come off easily.

But if the eggs are cold when you peel them then roll them to crack the shell a bit and put them into a bowl of warm water and peel in the water , the shell will come off easier .