The orbit of the Moon in 2013, viewed from the north pole of the ecliptic, with the vernal equinox to the right.

The orbit of the Moon in 2013, viewed from the north pole of the ecliptic, with the vernal equinox to the right.
The sizes of the Earth and Moon are exaggerated by a factor of 25. The frames include an alpha channel.

From this birdseye view, it's somewhat easier to see that the phases of the Moon are an effect of the changing angles of the sun, Moon and Earth. The Moon is full when its orbit places it in the middle of the night side of the Earth. First and Third Quarter Moon occur when the Moon is along the day-night line on the Earth.

The north pole of the Earth is tilted 23.5 degrees toward the 12 o'clock position at the top of the image. The tilt of the Earth is important for understanding why the north pole of the Moon seems to swing back and forth.

The widest swings happen when the Moon is at the 3 o'clock and 9 o'clock positions. When the Moon is at the 3 o'clock position, the ground we're standing on is tilted to the left when we look at the Moon. At the 9 o'clock position, it's tilted to the right. The tilt itself doesn't change. We're just turned around, looking in the opposite direction.

Animation and info via SVS NASA
http://svs.gsfc.nasa.gov/vis/a000000/a004000/a004000/

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