Well – my guess is that those folders actually exist on your computer and Picasa's display method is showing them next to each other.

There are several scenarios where you see what looks like duplicate folders:

1. If your filing system uses nested folders.  For example, I used to have a system where I created a folder for each year (2000, 2001, 2002 etc) then, within each folder I created January, February, March etc.  When viewing my pictures with Picasa in the 'Flat Folder View' it takes each individual folder and displays them alphabetically.  So I saw April, April, April, December, December, December etc.  If you choose to view using the Tree View, you will see that they are really 2000|April, 2001|April, 2002|April etc.  Watch video #17 Tree Structure in the Picasa Series.

2. You have folders with different resolutions of your pictures.  For example, if you get your photos from Walmart, and they give them to you on a disk – they give you more than one folder on that disk.  One folder will have all your pictures in their full-size resolution, one folder will have smaller size, or thumbnails.  If you copy everything from the disk to your computer, you will have two folders with what looks like duplicate contents. 

So, my point is, you need to investigate these duplicate folders further.  Use Picasa to right click on a picture and 'Locate on disk'  Then, notice the full path to the folder where that picture is located.  After doing that for a few different pictures in a few different 'duplicate' folders, you may realize what is going on. 

Picasa does not copy or move photos.  Try using Tree View and you may see where these 'duplicate' folders are coming from.