[This question involves mostly math papers, and may be relevant to graduate students learning to write and cite papers, although this is my only justification for this being a math question.]
Usually papers start out with the title and then the author. Sometimes near the author’s name there is the phrase “Communicated by John Doe”. Does this mean John Doe told the author the essentials of the paper and then the author wrote down the details? If so, why isn’t John Doe just a co-author? Or does this mean something else?
I could not find the answer using Google.
I’m posting my comment as an answer as Zev and amWhy asked me to do so:
It usually means that John Doe was the editor in charge. That is: John Doe received the submission by the author(s), contacted the referees and informed the board of editors about his and the referees’ opinion. John Doe thus takes some sort of responsibility on the paper. His name is associated with it and it’s his choice of the referees and his judgment of their opinion that ultimately led to the paper’s publication. However, John Doe doesn’t contribute a single line to the paper itself. Usually, the communicator is a rather senior and well-established mathematician.
Two journals that systematically use the “communicated by …” stamp are, among many others:
The CRAS are a journal that (at least historically) belongs to the category that Zev mentions in his answer. However, the Journal of Algebra shows that this is not necessarily the case. The explanation I’m giving tries to cover both cases.