A question about PDF Output settings

"Can someone explain what PDF Output options do and how they work in Illustrator?"

PDF settings have nothing to do with Illustrator other than they should honor your Illustrator Color Settings, Raster effects resolution, and fonts.  A PDF is a file type suitable for output ( in the case of print shops, that would be their RIP / Platemaker ). PDF stands for ( if I am not mistaken ) portable document format.  I have captured my Adobe Distiller "Press Quality" PDF Settings...

notice the "Resolution" is set for 5480 DPi.  I use these settings on all print jobs and never ran into any problems...

actually my "Monochrome Image Sampling is a little low, but still within reason.  I hould set it for 2740 DPi...

and your fonts should be embedded ( above )...

this is probably the most important setting ( for spot color especially ) "Leave Color Unchanged", mainly because you've already established your color swatches in Illustrator and you want them honored with no further manipulations...

and these ( above ) are user specific, but your print vendor may want some of these settings and may not want others...

last, but not least, Standards > None, again, your print vendor may want to chime in here, but by leaving it set to "none", you are leaving it open because, after all, you are in an open loop workflow ( when you send files out to be printed ).

These are my Distiller settings, but they should give you a better understanding of what to use in your given scenario.  One recommendation I make to new users or persons not that familiar with printing is to get Adobe's Print Publishing Guide, a very useful book about file prep and printing.