Machine coordinates set X/Y zero when your machine triggers its homing switches. So if you have limit switches, and click on "Ref All Home", your machine will move toward the direction of x=0, y=0 until it hits the homing switches, at which time it will set x=0, y=0 in the machine coordinates. You can think of machine coordinates as a x/y grid that starts from your gantry/router position when it is in the final "ref all home" postion.
Mach 3 can also keep a second grid in its head from the zero you set when you move your gantry/router to the position to correspond with the zero you set in your Aspire design in the material screen. Typically I set x/y=o in the center of my material. So after "ref all home", with the machine coordinates x/y=0, I move the axis to the center of the material, and click on x next to the digital read out, and y next to the digital readout, which sets x/y=0 in the work coordinates that measure everything from this new origin. Under the Digital readout (DRO), there is a button that is labeled "Machine Coords", if you click that it will go back and forth between the machine coordinates and the work coordinates. When the little red marker is lit under this label it means the read outs are showing machine coordinates.
ps - you can download the Mach3 manual from the ArtSoft website, and it will explain this and everything else much better than I can...http://www.machsupport.com/