What are Easter Eggs?

I've noticed a lot of games contain so called "Easter eggs", my question is simple. What are easter eggs in games?

According to Wikipedia:

A virtual Easter egg is an intentional hidden message, in-joke or feature in an object such as a movie, book, CD, DVD, computer program, web page or video game. The term was coined—according to Warren Robinett—by Atari after they were pointed to the secret message left by Robinett in the game Adventure.

Easter eggs are messages, videos, graphics, sound effects, or an unusual change in program behavior that sometimes occur in a software program in response to some undocumented set of commands, mouse clicks, keystrokes or other stimuli intended as a joke or to display program credits.

_{Easter egg (media) on Wikipedia}

TVTropes unsurprisingly has a huge list of examples.