I'm assuming you're only doing the design and not the actual implementation? In that case, PSD to HTML generally means that you need to provide the developer with all the assets and details they will need to actually convert your design into HTML.
Absolutely yes, it should have the complete, final, polished design of the site, but depending on your client and their dev, you might want to also include the site structure to make it clear where each link points to.
Putting all the photos, logos, icons, etc. on separate layers (preferably grouped appropriately for clarity) would come in very handy for any future design work, whether done by you or another designer, but you should probably check with your client as the developer might also want you to export all the assets out of the PSD. Including a list of all the fonts and colours used for elements such as the background or font colours and so on will also be very helpful for the dev and make sure that your design is implemented as closely as possible to what you envisioned.