The second computer is used only when running Swat, the debugger in the GEOS SDK.
You do all your coding and compiling on the host machine. Then you run the application on the target machine while you debug it.
That way, when your app crashes, it does not crash your host machine and you can use Swat to examine memory locations on the target machine or to backtrace to find the cause of the crash or hundreds of other useful things that Swat can do.
The target machine does not need to be a large or expensive machine. We recommend a 386 with at least one mb of RAM for speed's sake, but in practice you can use anything down to an XT level machine with only 640k if you're willing to wait a little bit.
Nowadays, you can pick up a used, or even a new, suitable target machine for just a very few hundred dollars. I've used some 286 systems as targets that cost less than $400 complete, and I've also run some 386's that were purchased second-hand for not much more than that.
Steve