There are two basic movement mechanisms that are used by CNC machines.
The first is a moving X-Y table moving under a tool that can move only in the Z direction (up and down). This mechanism was used by Nick Kennard in his machine.
Alternatively the tool is moved in the X-Y-Z directions. An example of such machine is the one built by Doug Costlow in his instructable .
Finally hybrids of the two types mentioned above exist, where a table moving only in the X direction whilst the tool moved in the Y and Z axes.
The first design was selected for this machine, basically because it is simplest to implement and as this is the first CNC machine that I have ever built. Also this design will result in a robust tool as the only possible movement is in the Z direction.