It is very common for non-lawyers to use the term "without prejudice" on legal letters for no other reason than they feel they should. This is not surprising given the mystique that has surrounded the law for so long but it is often used wrongly by lay people and sometimes even by lawyers who should know better!
Without Prejudice is properly used in the course of negotiations between parties who are trying to settle a dispute, often in the course of litigation but not necessarily. It means that neither party to the without prejudice correspondence can refer it to the court at a hearing or use it for any other purposes. It is therefore useful because the parties to a dispute are free to make offers which they wouldn't want a judge to know about.
Just because something is marked "without prejudice" doesn't mean anything. The party writing a without prejudice letter or email has to justify why it is properly marked with those words. Please also note that there are occasions where someone makes an admission of wrongdoing in a letter when "without prejudice" will not prevent the other party relying on that admission.
Then there's "without prejudice save as to costs" which we will save for another day.