The most common and most likely answer to this crossword clue is the 3 letter word FAX
I've seen this crossword clue in The Times
F
A
X
Buddy explains!
The straight part
We know that "Message" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case message = fax.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 FAX mean?
FAX noun- The hair of the head.
- A fax machine or a document received and printed by one.
- To send a document via a fax machine.