.u1conflict files appear when the document you have on your local machine is not the same as the one you have in your personal cloud and not the one you're uploading. In that case, Ubuntu One doesn't know which is the correct version and therefore syncs all of them, but makes it obvious that there are conflicts. That way, you're never in danger of getting the wrong version.
You will often see this problem when you're using LibreOffice to edit documents that are stored in a synced folder. The reason is that LibreOffice saves automatically at certain intervals, while Ubuntu One tries to sync all changes. This means it's very easy for you to be in the process of uploading a document when the local document changes. It seems that LibreOffice saves the document even when no changes have been made, which makes the problem worse.
Because of this, I would not recommend that you work on such files directly in a synced folder, but instead have a working directory and copy your files when you need them synced. This is not as elegant as it should be, but I think it's the best way for now. Someone has proposed a plugin for LibreOffice that makes it work better with Ubuntu One, but I don't think any work has been started on that yet. In any case, we should've had a good GUI to show the conflicts and to fix them. Sadly, I don't think we have that yet either.
So, in summary, conflict files are good. They make sure you never loose any data, even if your internet connection suddenly become very slow, for instance.