There is an entity C, such that the sentence "X is Y" is true, iff X=C.
This would produce the sentence "There is an entity C, such that "X wrote Waverley" is true, if and only if X=C; moreover, C is Scott". What Russell was getting at was that there was a problem with the traditional view that a definite description could be exchanged with a proper name. A phrase describing something (e.g. "the author of Waverley") means something different than a name (e.g. Scott) because while it is true that "George IV wanted to know if Scott was the author of Waverley", it is false that "George IV wanted to know if Scott was Scott". Russell's template solved this problem along with others like making claims about non-existent things. E.G. "The present king of France is bald" is problematic because there is no present king of France. If it were considered false then "The present king of France is not bald" would have to be considered true. This is avoided by saying instead: There is an entity C, such that the sentence 'X is French, bald, and kingly' is true iff X=C. THAT statement is false (because there is no entity that fits that description), and its opposite is true (i.e. There is NOT an entity...).
 pg 322, "Looking At Philosophy: The Unbearable Heaviness of Philosophy Made Lighter", 2005, Palmer
 Existence and Description, Bertrand Russell from "Metaphysics: an anthology" by Jaegwon Kim, Ernest Sosa - 1999