Full Idea
By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible.
Gist of Idea
The denotation of a definite description is flexible, rather than rigid
Source
John P. Burgess (Philosophical Logic [2009], 2.9)
Book Reference
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.35
A Reaction
This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid.