Theory and Analysis:Rei and the Moon
Throughout the series, Rei Ayanami is associated with the recurring visual motif of the Moon. In fact, the Moon is rarely shown in NGE without Rei in the foreground. Exceptions would be the shots of The Spear of Longinus heading towards the moon, and the "Moon's eye view" of Second Impact from Episode 21'.
Rei's left eye is specifically associated with the Moon. In Rei's monologue in Episode 14, this relation is brought up symbolically by a cut of Rei's eye blinking, followed by a cut to the moon.
Rei is a "vessel" for the soul of Lilith, and during First Impact 4 billion years ago, the Black Moon transporting Lilith collided with Earth, and Earth's Moon formed from the resulting debris. Thus, in a sense, Rei (or the soul of Lilith she carries) actually created the Moon.
The white giant in Terminal Dogma, who we later learn is, in fact, Lilith, wears a mask with crater-like markings. This serves to associate her with the Moon, and thus with Rei.