The most common and most likely answer to this crossword clue is the 9 letter word CARDBOARD
I've seen this crossword clue in The Daily Telegraph
C
A
R
D
B
O
A
R
D
Buddy explains!

The straight part
We know that "box material" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case box material = cardboard.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 CARDBOARD mean?
CARDBOARD noun- A wood-based material resembling heavy paper, used in the manufacture of boxes, cartons and signs.
- Made of or resembling cardboard; flat or flavorless.