'Dead Tree Format' is a literal, gently pejorative, way of referring to paper, or printed materials in general. It is often used to contrast them with electronic or cyber-materials, such as emails and sites and discourse on the Internet, or media such as radio and television that convey the same information appearing in a newspaper without requiring the pulpification of wood.
The phrase was popularized by the political correctness movement in being politically correct in its own blunt (but ecocentric) way. The phrase came into popularity around the same time that "dead animal flesh" or "non-human animal carcasses" were suggested as the politically correct alternatives for saying "meat".
Today this term for printed products is usually used by flamboyant environmentalists.