"Wax poetic" is reference to speaking with elevated, verbose, or romantic diction.
Wax is used in the same way that the phases of the moon are referred to - waxing and waning. Here, wax means to augment or grow. (from the old German wachsen - grow)
Exp: "Not to wax poetic, but such a sunset as this paints the beauty of the night sky with more dexterity than Van Gogh himself."