Theory invented by English philosopher and mathematician Bertrand Russell (1872-1970) in 1905 to show how denoting phrases like 'the present king of France' could still have meaning though there is nothing for them to denote.
Russell claimed that the grammatical form of 'The present king of France is bald' is misleading as to its logical form, which involves an existential claim; the sentence really says: 'There exists exactly one person reigning over France and there exists no person reigning over France who is not bald', which is false (because of its first clause) but uncontroversially meaningful.
Because the analysis of sentences should not depend on what happens to exist, Russell applied his analysis to all denoting phrases, calling most of them definite or indefinite descriptions (according to whether they involved the definite or indefinite articles (or their equivalents)). He also applied it to ordering proper names, which he treated as disguised descriptions.
The theory has been criticized as unnatural and unnecessary, but it and its ramifications have been immensely influential and are still current issues.
B Russell, 'On Denoting', Mind (1905); often reprinted