Author: Laz Marhenke <laz@leland.Stanford.EDU>

When it first formed, the Moon probably did not always show the same
face to the Earth.  However, the Earth's gravity distorts the Moon,
producing tides in it just as the Moon produces tides in the Earth.
As the Moon rotated, the slight elongation of its tidal bulge was
dragged a bit in the direction of its rotation, providing the Earth
with a "handle" to slow down the Moon's rotation.  More specifically,
the tidal bulge near the Earth is attracted to the Earth more strongly
than the bulge away from the Earth.  Unless the bulge points toward
the Earth, a torque is produced on the Moon.

If we imagine looking down on the Earth-Moon system from the north
pole, here's what we'd see with the Moon rotating at the same rate as
it goes around the Earth:

  Earth 					Moon
    __		
   /  \ 				       ____	      ^
  |    |				      /    \	      |
   \__/ 				      \____/	   Orbiting
							   this way
					 Tidal bulge *greatly*
					    exaggerated.


What if the Moon were rotating faster?  Then the picture would look like:

  Earth 					Moon
    __		
   /  \ 					___	      ^
  |    |				       /   )	      |
   \__/ 				      (___/        Orbiting
							   this way
					      Rotating
					  counterclockwise;
					 Tidal bulge *greatly*
					    exaggerated.

If it isn't clear why the tidal bulge should move the way the picture
shows, think about it this way: Take the Moon in the top picture, with
its tidal bulges lined up with the Earth.  Now, grab it and rotate it
counterclockwise 90 degrees.  Its tidal bulge is now lined up the
"wrong" way.  The Moon will eventually return to a shape with tidal
bulges lined up with the Earth, but it won't happen instantly; it will
take some time.  If, instead of rotating the Moon 90 degrees, you did
something less drastic, like rotating it one degree, the tidal bulge
would still be slightly misaligned, and it would still take some time
to return to its proper place.  If the Moon is rotating faster than
once per orbit, it's like a constant series of such little
adjustments.  The tidal bulge is perpetually trying to regain its
correct position, but the Moon keeps rotating and pushing it a bit out
of the way.

Returning to the second picture above, the Earth's gravitational
forces on the Moon look like this:
				 ___
		    F1	  <-----/   )
		    F2 <-------(___/

F2 is larger than F1, because that part of the Moon (the "bottom" half
in the drawing, or the half that's "rearward" in the orbit) is a bit
closer to the Earth.  As a result, the two forces together tend to
twist the Moon clockwise, slowing its spin.  Over time, the result is
that the Moon ends up with one face always facing, or "locked," to the
Earth.  If you drew this picture for the first case, (where the Moon
rotates at the same rate that it orbits, and the tidal bulges are in
line with the Earth), the forces would be acting along the same line,
and wouldn't produce any twist.

Another way to explain this is to say that the Moon's energy of
rotation is dissipated by internal friction as the Moon spins and its
tidal bulge doesn't, but I think the detailed force analysis above
makes things a little clearer.

This same effect occurs elsewhere in the solar system as well.  The
vast majority of satellites whose rotation rates have been measured
are tidally locked (the jargon for having the same rotation and
orbital periods).  The few exceptions are satellites whose orbits are
very distant from their primaries, so that the tidal forces on them
are very small. (There could be, in principle, other exceptions among
some of the close-in satellites whose rotation rates haven't been
measured, but this is unlikely as tidal forces grow stronger the
closer to the planet the satellite is.)

Pluto's satellite Charon is so massive (compared to Pluto) that it has
locked Pluto, as well as Pluto locking Charon.  This will happen to
the Earth eventually too, assuming we survive the late stages of the
Sun's evolution intact.  :')