Full Idea
Russell showed that his theory of definite descriptions affords solutions to each of four vexing logical problems: the Problems of Apparent Reference to Non-existents and Negative existentials, Frege's Puzzle about Identity, and Substitutivity.
Gist of Idea
Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity
Source
report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language 2.Over
Book Reference
Lycan,William G.: 'Philosophy of Language' [Routledge 2000], p.12
A Reaction
You must seek elsewhere for the explanations of the four problems, but this gives some indication of why Russell's theory was famous, and was felt to be a breakthrough in explaining logical forms.
Related Idea
Idea 10433 Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury]