Finder is creating "conflicted copy"s of files. What is this all about?

My finder is creating "conflicted copy"s of files on our network. We have 9 mac's (a law firm) and it appears that when another person opens a file, Mac sometimes creates a "conflicted copy". does anyone know why this is happening and what I can do to prevent this? I like nice neat folders and files and this is messin with my mojo!

Thank you!

Guy Vitetta

Charleston SC