Genesis is the first book of the Bible, and is believed to illustrate the creation of the world by God. The term literally translates to the beginning, or origin. The phrase Neon Genesis means new genesis, and suggests a restart and/or re-ordering of creation itself. Although the original genesis is never depicted in neither the series or the movies, the new genesis takes place during the climax of The End of Evangelion, in the form of the Third Impact. The purpose of the Human Instrumentality Project, is in fact to create a new genesis for mankind.
According to the Book of Genesis, God created the world in seven days: