Question

The narrator’s grandmother ‘could never have been pretty, but she was always beautiful’. Explain the importance of the statement.

Answer 1

'Pretty' and 'beautiful' are two words, often used interchangeably but which have quite distinct meanings.
To be pretty is to have attractive looks and often has a sexual connotation to it. Beautiful on the other hand is not just restricted to external appearance. It could be about having a wonderful personality.
The significance of this statement is to show the kind of respect and admiration that the narrator has towards his grandmother. It is not one that is based on transient looks but on a deeper personality that pulls him to her over the years. 

Answer 2

The statement of the author about his grandmother"she could never have been pretty but she was always beautiful" means that the author's grandmother did not have good looks or blonde hair but she had always had a beautiful heart and was an extremely caring person.