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An electronic Easter egg has very little to do with the celebration of the Christian holiday of Easter. It gets its 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 mountains of code, and 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 1980s 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 egg. (The alternative reason is so that it is not discovered and removed before the release of the program.) It is unlikely, therefore, that you will find an Easter egg unless you have been told specifically where to find it.
DVD Easter Eggs
More can be found out about Easter eggs at the Easter Egg Archive.