To me at least, an Axis here for CNC basically means a direction or dimension of travel. For example:
A single (1) axis system is basically where something, like the CNC cutting tool, can move left or right in a straight line, we can name this the X axis, X dimension or horizontal dimension.
Another way (2) to move the tool is in the up and down direction in a straight line (this is perpendicular or 90 degrees right angle from the horizontal dimension), we can name this the Y axis, Y dimension or vertical dimension.
And then there is another third (3) dimension that the tool can cut, and it is the Z axis or depth dimension, or Z dimension.
The computer will take the drawings and convert to them to a CNC code to run the stepper motors. (thats what I know from this site, since I do not have a CNC machine).
I seen some photos of CNC kits or machines for sale, already made if someone cannot get the materials or have the skill to make one. I dont have the link, but the one I seen had some small stepper motors that you find anyplace, unless they come with the kit.
This looks like a nice article about CNC to take a good look at: http://www.shopbottools.com/3-d_work_v2.htm
I found a link for some small metal milling machines:http://www.cncfusion.com/micromill1.html
SOME LINKS: http://www.cncfusion.com/Links.html
check out Camtronics with the 3d possibilities