The Dropbox app for Android doesn't save files to a "folder" like the PC version does. Android has stronger security and doesn't let apps access other apps' files, so even if it did do that, the browser wouldn't be able to read the image.
When you choose to open a file that's listed in Dropbox, the Dropbox app creates a special URI that points to that one file. It uses an intent to start an activity to view that URI, and sets a special flag to say that the new activity (in this case, the web browser) has permission to access only that URI. That means that there's no path you can put in the HTML file that lets the browser read the image: it has Dropbox's permission to read only the file you clicked on.
If you want to have a directory of HTML files and images that all load in the browser, you need to store it on the SD card (rather than in one app's data) where any app can read and write any file. I don't believe the Dropbox app has the feature of being able to sync directories on the SD card, but you could use another app to achieve that. For example, you could use an FTP client to sync the directory with one on an FTP server.
The answers to this question have lots of suggestions for how to keep directories in sync with Dropbox or another server.