All CNC machines have a "control" - that is to say, a computer which is responsible for interpreting G-code and orchestrating the movement and control of the axis motors, spindle, etc. High-end industrial machines tend to have dedicated embedded industrial controls with specialized user interfaces, specific to the task of running a machine. The Tormach represents the hobby end of the market, and as such takes a different approach, by using an off-the-shelf PC with specialized software and hardware to accomplish this task.
The Tormach control runs software called "PathPilot," which is an evolution of the open source LinuxCNC project that you may be familiar with. Their changes primarily are focused on providing their own customized and improved GUI over the basic LinuxCNC experience.
Both PathPilot and LinuxCNC run on standard x86 PC hardware, though the specific choice of hardware tends to be somewhat fussy due to constraints of the real-time Linux kernel used to provide reliable operation. To interface to the control electronics (stepper drivers, variable frequency drive for the spindle, limit switches, etc.), PathPilot depends on the use of an I/O card from Mesa (model 5i25 or 6i25). These cards provide reprogrammable FPGA engines for generation of step/direction pulses, offloading this task from the PC software, and providing more reliable timing in the process.
While PathPilot can run on a variety of PC hardware, this is a "known good" configuration shipped by Tormach: