The Konami Code was first used in the 1986 release of Gradius for the Nintendo Entertainment System. In a bit of gaming history, developer Kazuhisa Hashimoto, who was porting the 1985 arcade game Gradius to the NES, added the cheat code as he found it too difficult to play through during testing. The code gives a gamer a full set of power-ups. Famously, he forgot to remove it prior to release.
In the Google Play Games app, you simply swipe the screen in the ways: up, up, down, down, left, right, left, right. This is, of course, the way the NES controller was used to produce the cheat. At this point, since there are no dedicated A and B buttons on an Android device, the app will then display a dialog so you can finish with the required with B, A, and then Start.
After entering the code, you will get an achievement dubbed "All your game are belong to us." This is, of course, a reference to the equally historic Sega Mega Drive game Zero Wing and its arcane "All your base are belong to us."
A video demo of the Easter Egg is embedded.