Why doesn't the moon fall on earth? What causes an orbit?

There is a psydo-force called the centrafugal force, which is related to the velocity that an object is spinning (in this case around the earth).

 

If there was no gravity the moon would fly off in a stright line tangential to it's orbit. The force of gravity is continually accelerating the moon so that instead of doing this if falls towards the earth, but it's velocity tangentially to the earth is at the correct point so that the acceleration instead of putting the moon stright down it is in a curved fall that just happens to miss the earth, but misses it by enough so that it orbits in a relatively steady way.