Now that I remember...

I remember clearly that in one class the professor mentioned that he had to recompile our source codes in order to run the program. Does that mean that the executables created by us won't work on his computer? If so, and assuming he is also using linux, how is it possible for other machines to run software not compiled by them? It doesn't make sense. I download and run free software all the time, and I'm pretty sure I'm not getting any source code. I have to ask this on next class. This might come in the next exam if he asks about compilation. I mean, there must be something I can do when I compile my source code so that the executables work in any (or perhaps a broad range) of computers.