Picasa displays folders that are on your computer's disk and the photos those folders contain. Picasa works directly with the photos in the folders on your disk.
In Picasa's folder list, you will see:
Folders - the real folders on your computer's hard disk
"Green book" albums - built-in albums like the automatically maintained Starred Photos
Name Albums - built by the face recognition feature in Picasa
"Blue book" Albums - albums that you've explicitly created
"Purple book" folders for things you've created in Picasa like Collages and Movies
Folders have Manila Folder icons in Picasa's folder list (left side of the Library view). Hover the mouse over a folder icon that you see above thumbnails on the right side of the library view. You'll see the full path to that folder on disk. Click on that folder icon and you'll get a Windows Explorer window, opened to that folder on disk.
Picasa also shows you various "albums" - name albums, blue book albums, green book albums...
Albums exist only within Picasa
Albums do not contain their own copies of the photos they reference.
Albums simply point to photos. And photos always live in folders.
Albums help with photo organization.
A photo can appear in several albums. But that photo only exists in the folder. The albums are just referencing the photo, and so a photo that appears in several albums and one folder is not in any way duplicated. Although it will appear multiple times in Picasa.
What if different albums don't explain a photo showing up multiple times
There are two possible reasons. Either Picasa is "confused" and is showing "fake" doubles or... there are really doubles.
Please follow these steps to check if the duplicates are "real" or "fake":
Find two photos in folders (not in "blue book" or "green book" albums) that appear to be duplicates. Remember, albums NEVER cause duplicates.
For two suspected duplicate photos, right-click on each and and choose "Locate on Disk."
Windows Explorer will open for each photo. In Windows Explorer, you can see the full directory path to each photo and you can check if the photos are really duplicates or not.
After doing a "Locate on Disk" on the two photos and you discover that the two photos are actually the exact same photo on disk, then your Picasa database is probably corrupted. To fix the problem, just rebuilt the Picasa database following these directions:
https://sites.google.com/site/picasaresources/Home/Picasa-FAQ/picasa/how-to-rebuild-database
If the duplicates are real, check first if one of two paths aren't pointing to a backup folder that was accidentally added to Picasa. If this is the case, check "Tools"/"Folder manager" and set the backup folders to "Remove from Picasa".
If the duplicates are just copies that you want to get rid of, check out this: