The dropbox folder you see on your computer is just a reflection of what is on the dropbox server.
If you want to delete a file from dropbox but still have it on your computer, then try this (just on one file so you can follow the steps)
Make a folder on your desktop
Go to the dropbox folder on your computer
when you see the file you want to delete from Dropbox, then right click the file name , choose to COPY it and then paste it into the folder on your desktop. Check that the file is there and you are still able to open it.
If so, then NOW you can delete it from the dropbox folder, it then updates (synchs) with the server and that file has gone (but you still have it in the folder on the desktop)
I use dropbox a lot, I mainly use it for sending family history files/images to contacts - and once they confirm they have them saved on their computer I delete them from the dropbox folder which frees up space on my free account ( I transfer a lot of files this way).
BUT as I never 'move' a file into dropbox I just 'copy' it into there from where I have it stored on my hard drive and leave the original where it was so, if needed, I still have it in my family history files
Boo