I have been having the trouble of editing individual graphics. So if I edit a psd file will it edit the graphics within the html file?
No it won't. If you've been trying to edit a psd file that came with a template, and discovered that it doesn't affect the website then here's the reason why. The PSD file is just one of the files used when designing the site. It isn't one of the actual files in the end product.
PSD is the file type associated with photoshop. When graphic designers are making the site graphics they'll usually use photoshop (or compatible software) to create them. Once that's completed they'll save the individual sections for the website as jpeg,(or gif, or whatever). In the html file it'll use image tags to display the jpeg files. So if you want to change the look of your site, you'll need to change the jpeg files.
The easiest way to do that is if the template designer includes the original layered psd file. Then all you need to do is edit whatever layer you need to change and then save that as your new jpeg file. Then you'll copy your new jpeg over the old one on your server and your site will look how you want.
If you don't have the layered psd file to work with, then it's much more difficult to edit the jpegs themselves. If it's a very complicated design you might even have to just start over.
edit - so you're kind of right in your first post in thinking that the psd is kind of like an appendix that isn't necessary for a final website. But it's a very important file for anyone wanting to make changes to the design. Especially things like the text elements in a graphic design, or site logos, buttons, etc. Depending on the template design you might just have one psd file divided in sections, or you may have several for things like header, footer, buttons, etc.