a real world point of view
A Letter from the Doctor were short narratives, written as if by the Doctor himself.
The first letter appeared in the very first issue of Doctor Who Magazine and occasionally thereafter in special issues celebrating milestones in the publication's history.
More recently, "A Letter from the Doctor" was revived for the Annual-style publication, the Doctor Who Storybook. Most of the letters to date have been written by the show's producer and lead writer, Russell T Davies, with the exception of the Doctor Who Storybook 2009, when the letter was written by newly appointed showrunner Steven Moffat.
The letter in the Doctor Who Storybook 2010 -- written again by Davies -- is different in format from the others, appearing to be the transcription of a garbled transmission from the Doctor. It includes snippets of dialogue from Tenth Doctor TV episodes going back to the incarnation's very first words. Because of this format, it was believed the first words of the letter, "Don't forget me", might have been the last words of the Tenth Doctor in The End of Time. Ultimately, this was not the case; the final words spoken by him in that episode were, "I don't want to go". His final words to Sarah Jane Smith in TV: The Wedding of Sarah Jane Smith were, "Don't forget me".