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Full Idea
A phrase of the form 'a so-and-so' I shall call an 'ambiguous' description, and a phrase of the form 'the so-and-so' (in the singular) I shall call a 'definite' description.
Gist of Idea
The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description
Source
Bertrand Russell (Problems of Philosophy [1912], Ch. 5)
Book Ref
Russell,Bertrand: 'The Problems of Philosophy' [OUP 1995], p.28
A Reaction
This leaves the problem of those definite descriptions which succeed in referring ('the present Prime Minister'), those which haven't succeeded yet ('the person who will get the most votes'), and those which won't refer ('the present King of France').