For me, I only really got it after I had taken all three courses:

    - Machine Language 
    - Compiler Construction
    - Operating Systems

Just after that, a bunch of lightbulbs started to fire off. I think the NAND to Tetris approach is really great in this regard. It's designed to be the place where it all comes together for a Comp Sci person.

http://video.google.com/videoplay?docid=7654043762021156507