From our friends at Ask an Astonomer...
"...The Moon raises tides on the Earth. Because the side of the Earth that faces the Moon is closer, it feels a stronger pull of gravity than the center of the Earth. Similarly, the part of the Earth facing away from the Moon feels less gravity than the center of the Earth. This effect stretches the Earth a bit, making it a little bit oblong. We call the parts that stick out "tidal bulges." The actual solid body of the Earth is distorted a few centimeters, but the most noticable effect is the tides raised on the ocean.
Now, all mass exerts a gravitational force, and the tidal bulges on the Earth exert a gravitational pull on the Moon. Because the Earth rotates faster (once every 24 hours) than the Moon orbits (once every 27.3 days) the bulge tries to "speed up" the Moon, and pull it ahead in its orbit. The Moon is also pulling back on the tidal bulge of the Earth, slowing the Earth's rotation. Tidal friction, caused by the movement of the tidal bulge around the Earth, takes energy out of the Earth and puts it into the Moon's orbit, making the Moon's orbit bigger (but, a bit pardoxically, the Moon actually moves slower!).
This same process took place billions of years ago--but the Moon was slowed down by the tides raised on it by the Earth. That's why the Moon always keeps the same face pointed toward the Earth. Because the Earth is so much larger than the Moon, this process, called tidal locking, took place very quickly, in a few tens of millions of years"