Why is only one side of the moon visible from earth?

The moon is 'tidally locked' with earth. Planets and moons are not made of purely smoothe, evenly distributed material. They have lots of bumps and bulges, even if their over-all shape is spherical. The side of the moon that faces earth represents the more massive side of the moon. Over a very long time, the mutual tidal and gravitational forces between the earth and moon caused the more massive chunk of the moon to always face earth. All orbiting bodies have a tendency toward this tidal locking, but again, it takes an enormous amount of time and depends also on the rate of rotation of the body. 


Interestingly, there is something called 'libration', which causes the moon to apparently wobble from side to side and also a little up and down. [Think Libra, the scale. Imagine a balance scale slowly moving up and down until it settles.] The moon is not actually wobbling. The effect is the result of a practically constant rotational rate for the moon on its axis, and the fact that the orbital velocity of the moon around the earth is not constant. Because the moon's orbit is elliptical, the moon revolves more rapidly when it is closer to the earth. Also, some of the libration happens because the moon does not orbit around the earth exactly in the earth's equatorial plane. This means we can 'peak' a little above and a little below the usual view that we get of the moon. Over a period of about 15 years of lunar observation from earth, we can see very roughly 60% of the moon's surface as a result of all that libration.