Specifically, the discoloration is an indicator that the egg was overcooked, similar to how meat or rice might also get darker when overcooked.
What causes this color change?
Hydrogen sulfide from the egg white interacts with iron from the yolk. This process causes the change in color.

How do you avoid the green ring for good?
The key is to make sure to cook your hard boiled eggs for the correct amount of time.

How do you get the perfect hard boiled egg?
There’s a lot of controversy around the perfect time to cook hard boiled eggs, but consensus is between 10 to 12 minutes.
So next time you are ready to make hard boiled eggs, set yourself a cooking time or just use the timer on your phone. You’ll never see that green ring again.