An electronic easter egg has very little to do with the celebration of the Christian holiday of Easter. They get their name through a tenuous link to the practice of hiding Easter Eggs on Easter morning for children to try and find.

The Origins of Electronic Easter-Eggs

Computer programmers get little credit for many of the innovations they put into software, let alone the time they spend writing in the mountains of code. They are not always very pleased about it so as a result some enterprising software engineers have hidden extra credits within the software code.

Even some software from the early 1980's incorporated these hidden messages and as computer programming became increasingly dominated by impersonal corporations instead of small privately owned companies, there has been an explosion in the number of these Electronic Easter-Eggs.

Hiding Easter-Eggs

In order that the easter-egg doesn't get in the way of the running of the program there is often a complicated set of tasks to be accomplished in precisely the correct order so that you can access the easter-egg¹.
It is unlikely, therefore, that you will find an easter egg unless you have been told specifically where to find it.

More can be found out about Easter eggs at the Easter-Egg Archive