Where is my site actually stored? How can I move my Plone instance between different servers? What should I back up?
In which directories on the local host are the elements of the site actually stored? Which files do I need to back up? How do I move my Plone instance to a different server?
All content of your site is stored in your Data.fs file, normally located in your var/filestorage directory (var for non-buildout installs). (This depends on the platform you're on, do a search for Data.fs). The database is normally referred to as the Zope Object DataBase (ZODB).
This file is the entire database, and can be backed up by doing a simple copy. You can do this without shutting down your site, but for high-traffic sites that are live when you do the copy, you should use the repozo.py script that comes standard with Zope 2.7 or newer to do scheduled backups.
When doing backups, this is really the only critical file, but you may want to back up your buildout.cfg file and products and src directories too, to make sure you have the correct versions of them if you should need to restore your site.
To move your site from one server to another (for instance from a local Windows-based laptop to a centrally hosted Linux server), you can simply move the Data.fs file - as long as the Product versions that you are using are the same.
If you have a locally hosted Plone site and want to transfer it to your ISP, please be aware that your ISP has to support Plone hosting. It is possible to render a Plone site to static HTML using tools like CMFDeployment, but it is not recommended, as you lose a lot of the advantage of Plone's dynamic nature - and it is also a non-trivial setup exercise.