The most common and most likely answer to this crossword clue is the 5 letter word DOILY
I've seen this crossword clue in The Daily Telegraph
D
O
I
L
Y
More clues leading to the result DOILY
Buddy explains!

The straight part
We know that "napkin" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case napkin = doily.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DOILY mean?
DOILY noun- A small ornamental piece of lace or linen or paper used to protect a surface from scratches by hard objects such as vases or bowls; or to decorate a plate of food.
- An old kind of woollen material.