A letter starting with "Dear..." Saying that she (or he) doesn't love you anymore. About breaking up the relationship. The term "DearJohn" may have become common in WW II (Second World War) when american soldiers have been away from home for a long time, sometimes for years.

Oh! I saw a movie called 'Dear John' last night. I didn't know that it could have a meaning, except for someone starting a letter. Interesting question. See this link. http://www.dearjohn-movie.com/

It's an interesting term: http://dict.youdao.com/search?le=eng&q=dear+john+&tab=&keyfrom=dict.top