If two people change the same file at the same time, Dropbox won't try to merge the changes. Instead, it will save the original file as well as a second version which has the same name but is appended with "conflicted copy," the name of the person or computer responsible, and the date the conflict occurred. By creating a conflicted file, Dropbox ensures that all changes are preserved and nobody will overwrite another person's hard work.
Conflicted copies can also occur when a file is left open on another computer, especially when using applications with an auto-save feature. Closing the file from within the application on either computer should prevent further conflicts.
How can I prevent conflicted copies from happening in the future?
One workaround that can be used to prevent conflicted copies is to move the file out of the Dropbox folder while editing it. Doing this causes the file to appear as deleted and doesn't allow other users to edit the file. Once you're done editing, you can move the file back into its original location in the Dropbox folder. It will reappear with your edits for all users who have access to that file.
Another option is to move the file into a second folder designated for "In Use" files. Other members of the shared folder can still access it if they need to, but will know not to make changes.