--I commend you for hanging in there. When you said; "...but my goal... is to really to understand how the components work.", and then got for answers things like; "Don't worry about electronics" and "The LM317 has a build-in [sic] voltage reference.", I had the feeling that if you did not immediately shut up you were going to get the old kiss off, and I was right.
--Now, clearly you asked: "Yet I still don't quite get what the voltage reference is, or why it is required.". And the answer you got: "How else should it determine if the output voltage..." seemed to indicate that you were being argumentative, rather than seeking a rather more full explanation. Finally you were told to take up knitting.
--Please do not let the rude comments dissuade you from continuing to come to our wonderful forum. While DJ is busy trying to get people to join the forum, others are busy trying to run them off. There are lots of people here, who will help you and do not mind if a beginner is a tad ignorant (as I am), so please stay, You are indeed welcome.
--I found Olsenn's explanation, quite helpful as well. Please see below a link to download a PDF of the TI LM317 Data Sheet which has even more schematics, circuits, and explanations, you might find helpful.http://ebookbrowse.com/lm317-pdf-d136180503
--Also, If you would care for a laugh, check the below link, where an inquisitive poster is seeking help, and is advised to turn his design completely upside down, and then is, berated for not saying; "Thank you, Sir, may I have another"http://www.eevblog.com/forum/projects-designs-and-technical-stuff/creative-ideas-for-fuse-blown-indicator/
--In any case, stick around, take your shoes off.
"Does not squirrel crack nuts on bough of oak tree."
Lao Fu 1410 1620