In "A Mathematical Theory of Communication," Shannon successfully showed that channel capacity, electronic signals and noise can all be represented mathematically by using statistical functions, and thus can all be related to one another with statistics. This point is articulated by Franklin Institute Committee on Science and the Arts Chairman Tabor with the following:
"It seems to be agreed that thermal noise, atmospheric noise, and all of the kinds of what we have for many years called 'noise' can be described nicely by statistical functions...It seems to me that one of the most important things Shannon has done is to show how the signal can be described by statistical functions, so that signal and noise can both be handled simultaneously by the same mathematical methods."
Shannon's theory revolutionized the field of communication because it established a statistical relationship among the various elements of a communication system, allowing communication scientists to better understand the electronic relationships necessary for successful communication. Once they could better understand these relationships, they were better able to develop technologies that improved the field of communication. Conceiving of communication as a statistics-based science, as Shannon did, allowed for more precise calculations and more accurate communication methods.
You can read the full text of Tabor's letter, and the letter which he wrote in response to, by clicking on the thumbnails at right. The text of both letters speaks to the complicated nature of Shannon's theory, and shows that even the CSA committee members had difficulty grasping the concepts outlined in "A Mathematical Theory of Communication."