"Easter eggs" when used to talk about games are like special extras that aren't part of normal gameplay. Sometimes they're secret scenes, sometimes they're unlockable cheat codes. It can be anything really. You usually have to do something specific to unlock them.
For instance, in the case of Halo 3: if you've ever seen the hilarious web series Red vs Blue (which uses the Halo for machinima), they've put easter eggs into the game where you can actually talk/hear the voices of Red vs Blue characters while you're playing. The Red vs Blue series has nothing to do with the actual Halo plotline nor does it do anything extra except amuse the player who may know of the series.
