What it means
When a letter or conversation is marked "without prejudice", it means the parties are trying to negotiate a settlement and that what is said cannot later be used against either side in court. The purpose is to let people speak frankly and make compromise offers without fear that their willingness to settle will be treated as an admission. The protection only applies to genuine attempts to resolve a dispute — simply writing the words on a document does not automatically make it privileged.
How it's used
Their lawyer sent a without prejudice letter offering $10,000 to settle, knowing the figure could not be quoted to the judge if negotiations broke down.