The Konami code is one of those Easter eggs that has long since travelled outside of its origins. It first appeared in the seminal shooter Gradius in 1986, but came to prominence in the west thanks to the NES release of Contra (it is sometimes called "the Contra code"), and basically gives the players bonuses depending on the game: in Gradius you got all the power-ups, in Contra you got 30 lives.
Funnily enough, the code was intended as a debug tool, but someone forgot to remove it and, with Gradius in the latter stages of production...