Because the Moon is also orbiting around the Earth. If the Moon didn't rotate about its axis, here's what would happen. One side would be facing us right now; two weeks later, when the Moon has gone halfway in its orbit around the Earth, the opposite side of the Moon would be facing us. Here's a picture (the Earth and the Moon should really be spheres, of course, not squares):

     E A R T H
     E A R T H moon
     E A R T H moon
     E A R T H moon
     E A R T H

After the Moon has gone halfway in its orbit around the Earth, if the Moon didn't spin on its axis, the picture would look like this:

     E A R T H
moon E A R T H
moon E A R T H
moon E A R T H
     E A R T H

Notice that we on the Earth would now see the opposite side of the Moon (the Earth sees the "m" of "moon" in the first picture, but it sees the "n" of the word "moon" in the second picture).

What really happens is that the Moon is rotating on its axis; it spins once a month, exactly the same length of time as it takes to orbit the Earth. So, after half an orbit around the Earth, the Moon has also spun one-half of a revolution about its axis. The correct second picture looks like this:

     E A R T H
noom E A R T H
noom E A R T H
noom E A R T H
     E A R T H

Now the Moon has rotated 180 degrees, so the Earth still sees the "m" of "moon".

Here's another picture. After one-quarter of an orbit (about one week after the original picture), the Moon has rotated 90 degrees on its axis, and it looks something like this:

       n n n
       o o o
       o o o
       m m m
     E A R T H
     E A R T H
     E A R T H
     E A R T H
     E A R T H

Once again, the "m" side of "moon" is facing the Earth, but it took an appropriate amount of rotation of the Moon about its axis to keep the "m" side facing the Earth.

So the Moon rotates about its own axis in the same length of time that it takes to orbit the Earth. That's what keeps the same side of the Moon always facing the Earth.